Mathematical Methods in the Applied Sciences最新文献

{"title":"Inverse Coefficient Problems for Dynamic Equations on Time Scales","authors":"Ganesh Ashok Satpute, Syed Abbas","doi":"10.1002/mma.10872","DOIUrl":"https://doi.org/10.1002/mma.10872","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we have worked toward developing the theory for the inverse coefficient problems on an arbitrary time scale. We considered a general \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$$ n $$</annotation>\u0000 </semantics></math>th order linear dynamic equation \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>y</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 <mo>+</mo>\u0000 <msubsup>\u0000 <mrow>\u0000 <mo>∑</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>i</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <msub>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>i</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>y</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mi>i</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ {y}^{Delta^n}(t)+{sum}_{i=1}^n{p}_i(t){y}^{Delta^{n-i}}(t)=f(t) $$</annotation>\u0000 </semantics></math> on arbitrary time scale \u0000<span></span><math>\u0000 <mrow>\u0000 <mi>𝕋</mi>\u0000 </mrow>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"10114-10127"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parameter Identification Problem for the Abstract State-Dependent Delay Differential Equation","authors":"Santosh Ruhil,&nbsp;Muslim Malik","doi":"10.1002/mma.10811","DOIUrl":"https://doi.org/10.1002/mma.10811","url":null,"abstract":"<div>\u0000 \u0000 <p>In this manuscript, we deal with the first order identification problem for abstract state-dependent delay differential equation in a Banach space. The primary methods for identifying the results are a direct approach using Volterra integral equations for sufficiently regular data and an optimal control approach for less regular data. In optimal control approach, under certain hypotheses, the characterization of the limit of the sequence of approximate solutions demonstrates that it is a solution to the original identification problem. The abstract method finds relevance in various applications to partial differential equations (PDEs), providing further motivation for its exploration.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9469-9479"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Fast High-Order Nonpolynomial Spline Method for Nonlinear Time-Fractional Telegraph Model for Neutron Transport in a Nuclear Reactor","authors":"Priyanka,&nbsp;Anshima Singh,&nbsp;Sunil Kumar,&nbsp;Jesus Vigo-Aguiar","doi":"10.1002/mma.10840","DOIUrl":"https://doi.org/10.1002/mma.10840","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;The aim of the present study is to develop a fast high-order method for a nonlinear time-fractional telegraph model for neutron transport in a nuclear reactor. The discretization of the model involves the utilization of a fast Alikhanov formula for the time-fractional derivative and a high-order nonpolynomial spline scheme for the spatial variable. The proposed algorithm is computationally efficient with computational cost of \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;𝒪&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; and a storage requirement of \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;𝒪&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, where \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ M $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ N $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; represent the total number of grids in space and time, respectively. The stability and convergence of the developed method are established using the discrete energy approach in the \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {L}_2 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; norm. It is proved that the developed method converges with an order of \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;𝒪&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;mo&gt;.&lt;/mo&gt;\u0000 &lt;mn&gt;5&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9751-9769"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fixed-Point Results for (θ,G)-Quasirational Contraction in Triple Controlled Metric-Like Spaces With Applications","authors":"Sadia Farooq,&nbsp;Naeem Saleem,&nbsp;Maggie Aphane,&nbsp;Asima Razzaque","doi":"10.1002/mma.10854","DOIUrl":"https://doi.org/10.1002/mma.10854","url":null,"abstract":"<p>In this article, we provided fixed-point results for \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Θ</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ left(Theta, {G}_1right) $$</annotation>\u0000 </semantics></math>-quasirational contraction and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Θ</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ left(Theta, {G}_2right) $$</annotation>\u0000 </semantics></math>-quasirational contraction within the setting of triple controlled metric-like spaces. Furthermore, we demonstrate that this extension of spaces does not constitute a Hausdorff space. Our results are more generalized with respect to the existing ones in the literature. Additionally, we also discussed the existence and uniqueness of solution of Fredholm integral equation using our results within the setting of triple controlled metric-like spaces. In this sequel, we apply our primary finding to nonlinear fractional differential equations. Moreover, we introduce triple controlled metric-like spaces endowed with a graph, along with an open question.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9920-9933"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10854","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability Analysis of Impulsive Stochastic Systems With Poisson Jumps and Regime Switching","authors":"Daipeng Kuang,&nbsp;Shuihong Xiao,&nbsp;Jianli Li","doi":"10.1002/mma.10815","DOIUrl":"https://doi.org/10.1002/mma.10815","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper is devoted to discussing the \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;th-moment input-to-state stability (\u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-ISS), \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;th-moment integral-ISS (\u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-iISS), and \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;th-moment \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {e}&amp;#x0005E;{sigma t} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-ISS (\u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {e}&amp;#x0005E;{sigma t} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-\u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-ISS) for impulsive stochastic delayed differential system via the Lyapunov–Krasovskii functional and some analytical skills. For the fixed moment impulse, the results show that if the continuous dynamics is \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-ISS, then the system is \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-ISS with respect to a lower bound of the average impulsive interval. For the random moment i","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9520-9532"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Image Completion Using Automatic Structure Propagation With Bézier Curves","authors":"Petcharaporn Yodjai,&nbsp;Poom Kumam,&nbsp;Juan Martínez-Moreno","doi":"10.1002/mma.10826","DOIUrl":"https://doi.org/10.1002/mma.10826","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents an algorithm developed to fill the missing region of salient structures specifically for the curve. The stages are as follows: segmenting the image to identify the salient structures along with knowing the first and last points of each curve, finding a way to match points that should connect for structure reconstruction in missing salient structures, finding control points from the curve on the known region to estimate the control points in the missing curve to create a Bézier curve, and filling the missing regions of salient structures following the created Bezier curve. To choose candidate patches, we apply form image inpainting via modified exemplar-based inpainting with two-stage structure tensor, and image sparse representation method changes priority step as a product of data and confidence terms. Finally, find the candidate patch for better fill structures by rotating that original image to \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 <annotation>$$ r $$</annotation>\u0000 </semantics></math>-degree until a full 360°.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9598-9609"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enhancing Image Inpainting With Deep Learning Segmentation and Exemplar-Based Inpainting","authors":"Wachirapong Jirakitpuwapat,&nbsp;Kamonrat Sombut,&nbsp;Petcharaporn Yodjai,&nbsp;Thidaporn Seangwattana","doi":"10.1002/mma.10827","DOIUrl":"https://doi.org/10.1002/mma.10827","url":null,"abstract":"<div>\u0000 \u0000 <p>The technique of recreating faded or lost portions of an image is called image inpainting. A critical challenge in image inpainting is accurately identifying the areas that need reconstruction. This article explores the integration of deep learning segmentation to enhance the efficiency of image inpainting and exemplar-based inpainting methods using a two-stage structure tensor and image sparse representation to fill in missing areas. By leveraging advanced segmentation models, we can precisely delineate the areas requiring inpainting, allowing for more seamless and realistic restorations. Together, the exemplar-based inpainting method involves selecting filling order, maintaining structure, and blending candidate patches for natural results in object removal. Because we are using actual photographs, we do not compare between images after fill and solution. Therefore, we use the Mann–Whitney \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>U</mi>\u0000 </mrow>\u0000 <annotation>$$ U $$</annotation>\u0000 </semantics></math> test to compare efficiency approaches.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9610-9617"},"PeriodicalIF":2.1,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence, Uniqueness, and Averaging Principle for a Class of Fractional Neutral Itô–Doob Stochastic Differential Equations","authors":"Mohamed Rhaima,&nbsp;Lassaad Mchiri,&nbsp;Abdellatif Ben Makhlouf","doi":"10.1002/mma.10850","DOIUrl":"https://doi.org/10.1002/mma.10850","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper explores the existence, uniqueness, and averaging principles of neutral fractional stochastic Itô–Doob differential equations (NFSIDDEs). By utilizing the Picard iteration technique (PIT), we establish the existence and uniqueness of solutions. Additionally, we demonstrate the averaging principle for NFSIDDEs through the utilization of key inequalities, including the Gronwall and Hölder inequalities. Our findings contribute to a deeper understanding of the qualitative behavior and stability properties of NFSIDDEs, incorporating the fields of neutral fractional calculus, stochastic analysis, and classical inequalities.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9877-9886"},"PeriodicalIF":2.1,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Output-Feedback Stabilization for a Type of Stochastic Nonlinear Systems With Unknown Output Function and External Disturbances","authors":"Xiaoyan Qin,&nbsp;Wenhua Qiu","doi":"10.1002/mma.10853","DOIUrl":"https://doi.org/10.1002/mma.10853","url":null,"abstract":"<div>\u0000 \u0000 <p>This article investigates the output-feedback stabilization problem for a class of stochastic high-order systems with unknown output function and external disturbances. By combining the stochastic stability theorem, backstepping technique, and suitable Lyapunov function, an output-feedback controller is designed, incorporating both state controller and recursive full-order observer. So, an analytical method is proposed to address the challenges posed by the coupling of unknown output function and external disturbances for stochastic high-order nonlinear systems. And the provided controller can guarantee that the closed-loop system reaches the globally asymptotic stability in probability. Finally, the numerical simulation example is provided to show the efficacy of the proposed control approach.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9910-9919"},"PeriodicalIF":2.1,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Fractional Laplacian and Its Extension Problem","authors":"Salem Ben Said,&nbsp;Selma Negzaoui","doi":"10.1002/mma.10846","DOIUrl":"https://doi.org/10.1002/mma.10846","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, we establish four equivalent characterizations of the fractional Laplacian operator \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mo&gt;‖&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;‖&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {left(-leftVert xrightVert {Delta}_kright)}&amp;amp;amp;#x0005E;{sigma } $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ 0&amp;amp;lt;sigma &amp;amp;lt;1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, in some class of functions on \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℝ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathbb{R}}&amp;amp;amp;#x0005E;d $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Here, \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {Delta}_k $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denotes the Dunkl differential-difference Laplacian and \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ k $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a multiplicity function for the Dunkl operators. Starting from the natural Fourier characterization of \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mo&gt;‖&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;‖&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9840-9852"},"PeriodicalIF":2.1,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}