Mathematical Methods in the Applied Sciences最新文献

{"title":"An extended study of two multistep higher order convergent methods for solving nonlinear equations","authors":"Ramandeep Behl,&nbsp;Ioannis K. Argyros,&nbsp;Iñigo Sarria Martinez De Mendivil","doi":"10.1002/mma.10524","DOIUrl":"https://doi.org/10.1002/mma.10524","url":null,"abstract":"<p>The local analysis of convergence for two competing methods of order seven or eight is developed to solve Banach space-valued equations. Previous studies have used the eighth or ninth derivative of the operator involved, which do not appear on the methods, to show the convergence of these methods on the finite-dimensional Euclidean space. In addition, no computable error distances or isolation of the solution results are provided in this study. These problems limit the applicability of this method to solving equations with operators that are at least nine times differentiable. In the current study, only conditions on the first derivative, appearing in these methods, are employed to show the convergence of these methods. Moreover, computable error bounds depend on the distance in the world as well as the isolation of the solution. Results are provided based on generalized continuity conditions on the first derivative. Furthermore, the more interesting semi-local analysis of convergence not given before these methods is presented using a majorizing sequence. Finally, a great deal of impressive numerical results has been shown on real-world problems.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3907-3925"},"PeriodicalIF":2.1,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112888","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":"Monte Carlo safeguarding of key links through multiple random walks in large network","authors":"Qian Bai,&nbsp;Longfei Ni,&nbsp;Yongxin Zhang,&nbsp;Weibin Yao","doi":"10.1002/mma.10530","DOIUrl":"https://doi.org/10.1002/mma.10530","url":null,"abstract":"<p>Safeguarding important links is a useful way to promote network vulnerability, especially in sparse networks where random link failures can disconnect the network. Sustaining network connectivity is the main goal of safeguarding and can be handled by selectively safeguarding links belonging to certain cuts of a network. However, due to the inherent high complexity of cut enumeration, existing algorithms can only handle small-scale networks with limited nodes. It is important to find practical algorithms that are feasible for large-scale graphs, as a significant portion of real-world graphs under investigation are not as small as dozens of nodes. To address the problem, we propose to use a high-precision approximate approach to accelerate the first step of the two-step safeguard process and thus accelerate the whole process. A Monte Carlo algorithm is proposed to exploit efficient random paths for small cuts enumeration, which can help locate important edges with high probability in large-scale sparse networks. These edges will then be utilized to find the approximated minimum cost edge set whose safeguarding can sustain the expected network connectivity. The algorithm is validated using various sizes of graphs of random/Barbasi–Albert scale-free/Clustered scale-free/unit disk/Watts–Strogatz small-world and real-world graphs. The experimental results show that the algorithm can perfectly sustain the network connectivity, and the acceleration ratio of more than 10⁵ can be achieved with a little additional overhead. Specifically, in large graphs of one million nodes, approximated safeguard solutions survive at least 99.9% random link failures, and the solution time can be further reduced to dozens of seconds when the algorithm steps are easily implemented in full parallel.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3998-4014"},"PeriodicalIF":2.1,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112889","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":"Sliding mode control of the susceptible-exposed-asymptomatic-infected-recovered model with vaccination","authors":"Xi Chen,&nbsp;Changcheng Xiang,&nbsp;Yi Yang","doi":"10.1002/mma.10526","DOIUrl":"https://doi.org/10.1002/mma.10526","url":null,"abstract":"<p>This paper studies a nonlinear epidemiological model called susceptible, exposed, asymptomatic infected, infected, and recovered (SEAIR) with a control input (vaccination), which helps to design a sliding mode vaccination strategy by tracking the prevalence of infectious diseases. First, the effective reproduction number is adjusted to the expected value to control infectious disease outbreaks, even with model parameter changes and systematic perturbations. Meanwhile, based on the sliding mode control theory, two control strategies, namely, first-order sliding mode control and super-twisting control, are proposed to control the spread of COVID-19. Besides, an integral sliding surface associated with the effective reproduction number \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ {R}_0(t) $$</annotation>\u0000 </semantics></math> is constructed to eliminate the chattering problem of the system. Moreover, the sliding mode controller is robust to uncertainties and external perturbations. The stability and finite-time convergence of the closed-loop control system are verified by Lyapunov's second method. Also, the effect of the two control strategies on the system performance is evaluated by numerical simulations. Furthermore, this paper presents a practical case simulation based on data from Wuhan. The results indicate that universal vaccination is crucial in the early stage of the COVID-19 pandemic. As the epidemic progresses, vaccination is still an essential approach for epidemic prevention and control.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3936-3955"},"PeriodicalIF":2.1,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143111549","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":"Magnetized blood flow supported by tri-nanoparticles between a peristaltic curved conduit and endoscope","authors":"Essam M. Elsaid,&nbsp;Awatif J. Alqarni,&nbsp;Mohamed S. Abdel-wahed","doi":"10.1002/mma.10479","DOIUrl":"https://doi.org/10.1002/mma.10479","url":null,"abstract":"<p>In order to inspect the interior of hollow organs or cavities in the human body, endoscopes are frequently employed in medicine. Over time, they have undergone substantial evolution and are now able to offer invaluable diagnostic data. The non-invasive identification of tissue abnormalities with subcellular resolution or real-time biochemical information is made possible by novel endoscopic optical diagnostic methods. These methods provide benefits in terms of detection, characterization, and confirmation while challenging conventional histology. An investigation is conducted on a magnetized ternary nanofluid to analyze its heat production characteristics in a heated flow scenario between two curved conduits that are peristaltic and experience sinusoidal fluctuations. In this study, the use of a new peristaltic endoscope inside a curved conduit is examined, with a specific focus on evaluating the flowing behavior and heat transference attributes. The use of a versatile and innovative endoscope equipped with peristaltic locomotion proves to be a superior approach for conducting endoscopic procedures on intricate mechanical systems. Furthermore, this advanced endoscope offers enhanced comfort for patients undertaking endoscopy of various human parts. A detailed mathematical model has been constructed to fully assess the flowing and heat transference study of this innovative endoscope using the main unsteady regulating formulas like impetus, Maxwell, and heat in their general form, then transformed to a non-dimensional system with the assumption of a low Reynold's number and wavelength. Mathematica software was used to conduct precise and methodical calculations, enabling the acquisition of both accurate mathematical results and graphical representations. According to certain findings, the conduit is more influenced by the magnetized force, and the pressure rate over the channel width changes from a linear relationship to a sharp curve that ends in a small peak. Additionally, when utilizing different kinds of nanoparticles, there is a noticeable increase in the pressure gradient's magnitude.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3170-3189"},"PeriodicalIF":2.1,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143111670","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":"The Fujita exponent for a semilinear heat equation with forcing term on Heisenberg group","authors":"Meiirkhan B. Borikhanov,&nbsp;Michael Ruzhansky,&nbsp;Berikbol T. Torebek","doi":"10.1002/mma.10514","DOIUrl":"https://doi.org/10.1002/mma.10514","url":null,"abstract":"<p>In this paper, we study a critical exponent to the semilinear heat equation with forcing term on Heisenberg group. Our technique of proof is based on methods of nonlinear capacity estimates specifically adapted to the nature of the Heisenberg group. The critical exponent will be bounded for all dimensions of the Heisenberg group, in contrast to the Euclidean case which in the 1D and 2D cases will be infinite. In addition, we give an upper bound estimate on the lifespan of local solutions.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3794-3810"},"PeriodicalIF":2.1,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143111552","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":"Global existence and asymptotic behavior of affine solutions to Navier–Stokes equations in \u0000ℝN with degenerate viscosity and free boundary","authors":"Kunquan Li","doi":"10.1002/mma.10520","DOIUrl":"https://doi.org/10.1002/mma.10520","url":null,"abstract":"<p>This paper is concerned with affine solutions to the isentropic compressible Navier–Stokes equations with physical vacuum free boundary. Motivated by the result for Euler equations by Sideris (Arch Ration Mech Anal 225:141–176, 2017), we established the existence theories of affine solutions for the Navier–Stokes equations in \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ {mathrm{mathbb{R}}}&amp;amp;amp;#x0005E;Nleft(Nge 2right) $$</annotation>\u0000 </semantics></math> space under the homogeneity assumption that the pressure and the nonlinear viscosity parameters as functions of the density have a common degree of homogeneity. We derived an \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>×</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$$ Ntimes N $$</annotation>\u0000 </semantics></math> second-order system of nonlinear ODEs of the deformation gradient \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ A(t) $$</annotation>\u0000 </semantics></math> and provided an asymptotic analysis of the corresponding matrix system. The results show that both the diameter and volume of viscous fluids expand to infinity as time goes to infinity, and the algebraic rate of expansion is not bigger than that of inviscid fluids (Euler equations). In particular, the results contain the spherically symmetric case, in which the free boundary will grow linearly in time, exactly as that in inviscid fluids. Moreover, these results can be applied to the Navier–Stokes equations with constant viscosity and the Euler equations.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3871-3894"},"PeriodicalIF":2.1,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143111547","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 new approach to the directional derivative of fractional order","authors":"Aykut Toplama","doi":"10.1002/mma.10525","DOIUrl":"https://doi.org/10.1002/mma.10525","url":null,"abstract":"<p>The fractional derivative approximations offer many approaches to understanding real-world problems. The conformable fractional derivative operator that is one of the fractional derivative operators has recently attracted a lot of interesting. In this paper, a new approach to the directional derivative obtained with the help of the conformal fractional derivative is presented. Considering this approach, the definition of the fractional partial derivative is reformulated. In addition, a new definition of fractional gradient, fractional curl, and fractional divergence is given, and the properties of these new concepts are examined.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3926-3935"},"PeriodicalIF":2.1,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10525","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110794","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":"Sinc method in spectrum completion and inverse Sturm–Liouville problems","authors":"Vladislav V. Kravchenko,&nbsp;L. Estefania Murcia-Lozano","doi":"10.1002/mma.10478","DOIUrl":"https://doi.org/10.1002/mma.10478","url":null,"abstract":"&lt;p&gt;Cardinal series representations for solutions of the Sturm–Liouville equation \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;q&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;mi&gt;y&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ρ&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;y&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ -{y}&amp;#x0005E;{prime prime }&amp;#x0002B;q(x)y&amp;#x0003D;{rho}&amp;#x0005E;2y,xin left(0,Lright) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with a complex-valued potential \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;q&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;annotation&gt;$$ q(x) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are obtained, by using the corresponding transmutation operator. Consequently, partial sums of the series approximate the solutions uniformly with respect to \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ rho $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in any strip \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;Im&lt;/mtext&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ left&amp;#x0007C;operatorname{Im}kern0.1em rho right&amp;#x0007C;&amp;lt;C $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of the complex plane. This property of the obtained series representations leads to their applications in a variety of spectral problems. In particular, we show their applicability to the spectrum completion problem, consisting in computing large sets of the eigenvalues from a reduced finite set of known eigenvalues, without any information on the potential \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3130-3169"},"PeriodicalIF":2.1,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110592","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":"An efficient numerical method for the distributed-order time-fractional diffusion equation with the error analysis and stability properties","authors":"Safar Irandoust-Pakchin,&nbsp;Mohammad Hossein Derakhshan,&nbsp;Shahram Rezapour,&nbsp;Mohamed Adel","doi":"10.1002/mma.10459","DOIUrl":"https://doi.org/10.1002/mma.10459","url":null,"abstract":"<p>In this manuscript, we study and examine the time-fractional modified anomalous sub-diffusion model of distributed-order. Two numerical approaches are used to study the approximate solutions of the presented model. For the first approach, we use a second-order difference method based on the L1 formula for the temporal variable. In this case, stability and convergence analysis for time discretization using the L1 formula is displayed. For the second approach, we display and demonstrate the numerical method for the full-discrete based on the Galerkin weak form based on various kernels and shape functions of reproducing kernel particle method which do not have the \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 <annotation>$$ delta $$</annotation>\u0000 </semantics></math>-Kronecker property. Moreover, in this manuscript, in order to be able to use the necessary boundary conditions, the two straight strategies are used: one is the Lagrange multiplier method, and the other one is the penalty method. By using penalty method, we can the main boundary value model is changed to a new BVP with Robin boundary condition. At the end of the article, some numerical examples are presented and analyzed for the efficiency of the proposed numerical method. Also, the presented numerical method is compared with other numerical approaches, and the results of this comparison are reported in the form of a table.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"2743-2765"},"PeriodicalIF":2.1,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143121442","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":"Borel transform and integral identities involving λ-Bessel and λ-Tricomi matrix functions","authors":"Umme Zainab,&nbsp;Manoj Kumar,&nbsp;Nusrat Raza","doi":"10.1002/mma.10483","DOIUrl":"https://doi.org/10.1002/mma.10483","url":null,"abstract":"<p>This paper focuses on integrals and Borel transforms concerning \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 <annotation>$$ lambda $$</annotation>\u0000 </semantics></math>-Bessel and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 <annotation>$$ lambda $$</annotation>\u0000 </semantics></math>-Tricomi functions, employing an umbral perspective as a central approach. Differintegral techniques, presently utilized in calculus, offer a rich reserve of tools that can be utilized across a broad spectrum of problems encompassing the realm of special functions and beyond. Employing integral transforms akin to the Borel type and the related formalism proves to be a potent approach, facilitating a connection between umbral and operational methodologies. By integrating these perspectives, we establish a novel and effective method for deriving integrals of hybrid special functions and achieving the summation of their corresponding generating functions.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"3253-3271"},"PeriodicalIF":2.1,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143121244","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}