Mathematical Methods in the Applied Sciences最新文献

{"title":"Solving generalized nonlinear functional integral equations with applications to epidemic models","authors":"Sukanta Halder,&nbsp; Vandana,&nbsp; Deepmala","doi":"10.1002/mma.10437","DOIUrl":"https://doi.org/10.1002/mma.10437","url":null,"abstract":"<p>In this article, we investigate the existence and uniqueness of solutions to a generalized nonlinear functional integral equation (G-NLFIE) associated with certain epidemic models of infectious diseases, defined within the Banach space \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <mo>[</mo>\u0000 <mn>0,1</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$$ Cleft[0,1right] $$</annotation>\u0000 </semantics></math>. Our existence results include several specific cases of nonlinear functional integral equations that commonly occur in nonlinear sciences. We then introduce an iterative algorithm that combines Adomian's decomposition method (ADM) with the modified homotopy perturbation method (mHPM) to approximate solutions to the G-NLFIE. The paper addresses the convergence properties and error analysis of this method. Finally, we present numerical examples to demonstrate the effectiveness and efficiency of our proposed approach.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2318-2337"},"PeriodicalIF":2.1,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862351","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":"Curves defined by a class of discrete operators: Approximation result and applications","authors":"Rosario Corso,&nbsp;Gabriele Gucciardi","doi":"10.1002/mma.10441","DOIUrl":"10.1002/mma.10441","url":null,"abstract":"<p>In approximation theory, classical discrete operators, like generalized sampling, Szász-Mirak'jan, Baskakov, and Bernstein operators, have been extensively studied for scalar functions. In this paper, we look at the approximation of curves by a class of discrete operators, and we exhibit graphical examples concerning several cases. The topic has useful implications about the computer graphics and the image processing: We discuss applications on the approximation and the reconstruction of curves in images.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2388-2403"},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10441","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220061","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":"Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions","authors":"A. Kirsch,&nbsp;B. Schweizer","doi":"10.1002/mma.10435","DOIUrl":"10.1002/mma.10435","url":null,"abstract":"<p>We study the Helmholtz equation with periodic coefficients in a closed waveguide. A functional analytic approach is used to formulate and solve the radiation problem in a self-contained exposition. In this context, we simplify the non-degeneracy assumption on the frequency. Limiting absorption principles (LAPs) are studied, and the radiation condition corresponding to the chosen LAP is derived; we include an example to show different LAPs lead, in general, to different solutions of the radiation problem. Finally, we characterize the set of all bounded solutions to the homogeneous problem.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2267-2293"},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10435","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220060","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":"Sobolev-type regularization method for the backward diffusion equation with fractional Laplacian and time-dependent coefficient","authors":"Tran Thi Khieu,&nbsp;Tra Quoc Khanh","doi":"10.1002/mma.10425","DOIUrl":"10.1002/mma.10425","url":null,"abstract":"<p>This work is concerned with an ill-posed problem of reconstructing the historical distribution of a backward diffusion equation with fractional Laplacian and time-dependent coefficient in multidimensional space. The investigated problem is regularized by a Sobolev-type equation method. Unlike previous works, to prove the convergence of the regularized solution to the exact one, we only require a very weak and natural a priori condition that the solution belongs to the standard Lebesgue space \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ {L}&amp;amp;amp;#x0005E;2left({mathrm{mathbb{R}}}&amp;amp;amp;#x0005E;dright) $$</annotation>\u0000 </semantics></math>. This is done by suitably employing the Lebesgue-dominated convergence theorem. If we go further to impose a stronger a priori condition, one may know how fast the convergence is. Finally, some MATLAB-based numerical examples are provided to confirm the efficiency of the proposed method.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2085-2101"},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220067","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":"Oscillatory systems with two degrees of freedom and van der Pol coupling: Analytical approach","authors":"Sinisa Kraljevic,&nbsp;Miodrag Zukovic,&nbsp;Livija Cveticanin","doi":"10.1002/mma.10446","DOIUrl":"10.1002/mma.10446","url":null,"abstract":"<p>In this paper steady-state vibrations of the two-degrees-of-freedom oscillatory systems with van der Pol coupling are investigated. The model is a system of two differential equations with weak nonlinearity. A new solving procedure based on D′Alembert's method and the method of time-variable amplitude and phase is developed. The main advantage of the method in comparison to others is that it gives the solution of the system of two coupled weak nonlinear equations in the form that is simple to analyze, as it has the same form as the solution of the corresponding system of linear equations. In the paper two types of systems are considered: one, a two-mass system with two degrees of freedom, and second, the one-mass system with two degrees of freedom. The torsional vibrations of a two-mass system and vibrations of a Jeffcott rotor with two-degrees-of-freedom are analyzed. Analytically obtained results are numerically tested. It is obtained that the difference between analytic and numeric results is small and almost negligible. As the accuracy of the analytic solution is high, it is suitable for application in technics and engineering. Conclusions about steady-state self-sustainable oscillators, orbital, and limit cycle motions are given.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2474-2492"},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220066","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":"Time delays in a double-layered radial tumor model with different living cells","authors":"Yuanyuan Liu,&nbsp;Yuehong Zhuang","doi":"10.1002/mma.10456","DOIUrl":"10.1002/mma.10456","url":null,"abstract":"&lt;p&gt;This paper deals with the free boundary problem for a double-layered tumor filled with quiescent cells and proliferating cells, where time delay \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ tau &amp;amp;gt;0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in cell proliferation is taken into account. These two types of living cells exhibit different metabolic responses and consume nutrients \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ sigma $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; at different rates \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;λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {lambda}_1 $$&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;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&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;$$ {lambda}_2 $$&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;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&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;$$ {lambda}_1leqslant {lambda}_2 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;). Time delay happens between the time at which a cell commences mitosis and the time at which the daughter cells are produced. The problem is reduced to a delay differential equation on the tumor radius \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ R(t) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; over time, and the difficulty arises from the jump discontinuity of the consumption rate function. We give rigorous analysis on this new model and study the dynamical behavior of the global solut","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2655-2664"},"PeriodicalIF":2.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220062","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":"On a parabolic equation in microelectromechanical systems with an external pressure","authors":"Lingfeng Zhang,&nbsp;Xiaoliu Wang","doi":"10.1002/mma.10427","DOIUrl":"10.1002/mma.10427","url":null,"abstract":"&lt;p&gt;The parabolic problem \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;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;f&lt;/mi&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;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&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;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {u}_t-Delta u&amp;amp;amp;#x0003D;frac{lambda f(x)}{{left(1-uright)}&amp;amp;amp;#x0005E;2}&amp;amp;amp;#x0002B;P $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on a bounded domain \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ Omega $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; 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;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}&amp;amp;amp;#x0005E;n $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with Dirichlet boundary condition models the microelectromechanical systems (MEMS) device with an external pressure term. In this paper, we classify the behavior of the solutions to this equation. We first show that under certain initial conditions, there exist critical constants \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;P&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {P}&amp;amp;amp;#x0005E;{ast } $$&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;msubsup&gt;\u0000 &lt;mrow","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2122-2140"},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220064","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":"Three minimal norm Hermitian solutions of the reduced biquaternion matrix equation \u0000EM+M˜F=G","authors":"Sujia Han,&nbsp;Caiqin Song","doi":"10.1002/mma.10424","DOIUrl":"10.1002/mma.10424","url":null,"abstract":"<p>In this paper, we investigate the minimal norm Hermitian solution, pure imaginary Hermitian solution and pure real Hermitian solution of the reduced biquaternion matrix equation. We introduce the new real representation of the reduced biquaternion matrix and the special properties of \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mi>e</mi>\u0000 <mi>c</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>Ψ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mi>M</mi>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ Vecleft({Psi}_{PMQ}right) $$</annotation>\u0000 </semantics></math>. We present the sufficient and necessary conditions of three solutions and the corresponding numerical algorithms for solving the three solutions. Finally, we show that our method is better than the complex representation method in terms of error and CPU time in numerical examples.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2064-2084"},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220069","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":"Optimal control strategies for infectious diseases with consideration of behavioral dynamics","authors":"Omar Forrest,&nbsp;Mo'tassem Al-arydah","doi":"10.1002/mma.10388","DOIUrl":"10.1002/mma.10388","url":null,"abstract":"<p>We present a simple SVIR (susceptible, vaccinated, infected, recovered) model to analyze the spread of COVID-19, incorporating the influence of the population's caution on the transmission rate, which is considered nonlinear in current number of infected. Demonstrating a positive bound solution confirms the model's biological relevance. Through a formula for the basic reproduction number, we explore the local asymptotic stability of the disease-free equilibrium (DFE) and endemic equilibrium (EE), showing that the existence of the EE relies on the basic reproduction number. Furthermore, we establish the global stability of the DFE by constructing a Lyapunov function. We present an optimal control problem for vaccination, demonstrating the existence and uniqueness of the optimal strategy. Our simulations indicate that optimal vaccination is effective in reducing infections and costs. We also investigate the effect of integrating education into the model to underscore its importance in decreasing disease transmission rates and reducing the necessity for vaccine uptake.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1362-1380"},"PeriodicalIF":2.1,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10388","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220063","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":"On time-fractional partial differential equations of time-dependent piecewise constant order","authors":"Yavar Kian,&nbsp;Marián Slodička,&nbsp;Éric Soccorsi,&nbsp;Karel Van Bockstal","doi":"10.1002/mma.10439","DOIUrl":"10.1002/mma.10439","url":null,"abstract":"<p>This contribution considers the time-fractional subdiffusion with a time-dependent variable-order fractional operator of order \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ beta (t) $$</annotation>\u0000 </semantics></math>. It is assumed that \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ beta (t) $$</annotation>\u0000 </semantics></math> is a piecewise constant function with a finite number of jumps. A proof technique based on the Fourier method and results from constant-order fractional subdiffusion equations has been designed. This novel approach results in the well-posedness of the problem.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2354-2369"},"PeriodicalIF":2.1,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220093","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}