Partial Differential Equations in Applied Mathematics最新文献_第2页

An analytical solution to the fractional Fredholm–Volterra Integro-differential equation using the limit residual function technique

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-10 DOI: 10.1016/j.padiff.2025.101121

Aliaa Burqan , Ahmad El-Ajou

{"title":"An analytical solution to the fractional Fredholm–Volterra Integro-differential equation using the limit residual function technique","authors":"Aliaa Burqan , Ahmad El-Ajou","doi":"10.1016/j.padiff.2025.101121","DOIUrl":"10.1016/j.padiff.2025.101121","url":null,"abstract":"<div><div>The primary objective of this study is to develop an analytic solution for mixed integrodifferential equations of fractional order, which are commonly applied in the mathematical modeling of various physical phenomena. This work introduces a novel approach based on the limit of the residual function, resulting in a convergent series expansion for the solutions. The new method has the advantage of quickly determining the coefficients of the series solution and the limited calculations required compared to other methods. The article presents and discusses various applications to validate the theoretical findings. These applications cover three types of fractional integrodifferential equations: the Fredholm integrodifferential equation, the Volterra integrodifferential equation, and the Fredholm-Volterra integrodifferential equation. The results demonstrate a strong agreement between the exact and approximate solutions. A key feature of this proposed method is that it does not necessitate any unreasonably restrictive assumptions, such as perturbation, linearization, or guessing initial data. This makes it a practical tool for directly solving nonlinear fractional problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101121"},"PeriodicalIF":0.0,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The stretch coordinate effect, bifurcation, and stability analysis of the nonlinear Hamiltonian amplitude equation

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-10 DOI: 10.1016/j.padiff.2025.101126

S M Rayhanul Islam , Md. Ekramul Islam , M. Ali Akbar , Dipankar Kumar

{"title":"The stretch coordinate effect, bifurcation, and stability analysis of the nonlinear Hamiltonian amplitude equation","authors":"S M Rayhanul Islam , Md. Ekramul Islam , M. Ali Akbar , Dipankar Kumar","doi":"10.1016/j.padiff.2025.101126","DOIUrl":"10.1016/j.padiff.2025.101126","url":null,"abstract":"<div><div>The new Hamiltonian amplitude equation effectively expresses the modulated wave instability and addresses the ill-posedness of the unstable nonlinear Schrödinger equation. This equation simulates nonlinear optical pulse propagation, fiber optic communication engineering, self-phase modulation, and modulated wave train instability. The unified tanh approach is used in this article to establish broad-spectral soliton solutions to the stated model in terms of hyperbolic and trigonometric functions. The solutions enfolded several free parameters associated with the model and the procedure, and specific values of these parameters result in some novel and typical soliton solutions that are examined in the texts. Additionally, the effect of the stretch coordinate ε is examined. The effects of stretching coordinates are determined by sketching three- and two-dimensional plots for different values of ε. The stability analysis of the gained solutions is examined, and the Hamiltonian function is discussed. Furthermore, we proceed to the bifurcation analysis of the model that is explored. To analyze the dynamic behavior of the solitons in nonlinear optics and other fields, the stability of the equilibrium points is evaluated, and a graphical representation of the system's phase diagram is provided.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101126"},"PeriodicalIF":0.0,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of the solitary wave solutions of the negative order modified Korteweg –de Vries equation with a self-consistent source

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-08 DOI: 10.1016/j.padiff.2025.101108

G.U. Urazboev , I.I. Baltaeva , Sh.E. Atanazarova

引用次数: 0

Existence of solutions of multi-order fractional differential equations

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-07 DOI: 10.1016/j.padiff.2025.101104

Faycal Bouchelaghem , Hamid Boulares , Abdelouaheb Ardjouni , Fahd Jarad , Thabet Abdeljawad , Bahaaeldin Abdalla , Kamal Shah

引用次数: 0

Quantum-assisted hλ-adaptive finite element method

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-07 DOI: 10.1016/j.padiff.2025.101120

R.H. Drebotiy, H.A. Shynkarenko

{"title":"Quantum-assisted hλ-adaptive finite element method","authors":"R.H. Drebotiy, H.A. Shynkarenko","doi":"10.1016/j.padiff.2025.101120","DOIUrl":"10.1016/j.padiff.2025.101120","url":null,"abstract":"<div><div>Quantum computing is a rapidly advancing field, driven by the potential advantages derived from the unique properties of quantum entanglement. In particular, the exponential speedup of certain carefully designed algorithms, compared to their classical counterparts, promises to significantly enhance the numerical solution of a wide range of problems.</div><div>This paper investigates the integration of quantum computing with the finite element method, focusing on singularly perturbed advection-diffusion-reaction problems. We introduce a novel finite element scheme that combines classical and quantum algorithms. In this approach, the primary mesh adaptation loop is managed by a classical computer, while a specific stabilization procedure is executed on a quantum computer. This procedure leverages the Harrow-Hassidim-Lloyd algorithm in conjunction with the swap test to estimate the value of a linear functional, which constitutes a substantial portion of the computational workload.</div><div>We demonstrate that this hybrid approach effectively eliminates parasitic oscillations in the finite element approximation, even at the early stages of the adaptation process. This leads to a significant improvement in the quality of intermediate finite element solutions. As a result, our scheme offers more efficient feedback with reduced computational costs for researchers using the method to investigate physical phenomena. To support the scheme, we prove special explicit a posteriori error estimates. Possible benefits of the proposed finite element scheme are analyzed using the numerical comparison with the typical adaptive scheme.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101120"},"PeriodicalIF":0.0,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Atomic solutions to Bateman–Burgers type equation via tensor products

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-06 DOI: 10.1016/j.padiff.2025.101102

Afaf Alhawatmeh , Mohammad Al Bataineh , Naba Alashqar , Roshdi Khalil

引用次数: 0

Haar wavelet Arctic Puffin optimization method (HWAPOM): Application to logistic models with fractal-fractional Caputo-Fabrizio operator

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-06 DOI: 10.1016/j.padiff.2025.101114

Najeeb Alam Khan , Sahar Altaf , Nadeem Alam Khan , Muhammad Ayaz

{"title":"Haar wavelet Arctic Puffin optimization method (HWAPOM): Application to logistic models with fractal-fractional Caputo-Fabrizio operator","authors":"Najeeb Alam Khan , Sahar Altaf , Nadeem Alam Khan , Muhammad Ayaz","doi":"10.1016/j.padiff.2025.101114","DOIUrl":"10.1016/j.padiff.2025.101114","url":null,"abstract":"<div><div>This study introduces a novel hybrid numerical methodology for approximating differential equations involving the fractal-fractional Caputo-Fabrizio (FFCF) operator, which is an essential tool for modelling complex dynamical systems involving memory effects. The proposed method integrates the Haar wavelet with the Arctic Puffin optimization (APO) algorithm, a meta-heuristic optimization inspired by the foraging behavior of Arctic Puffins. The Haar wavelet, well-known for its compact support and piecewise constant characteristics, is based on the Haar basis functions used to construct an operational matrix for the FFCF operator. These matrices transform the differential equations into a system of algebraic equations involving unknown coefficients, and then optimize them using the APO algorithm, ensuring efficient and accurate solutions. Two nonlinear quadratic and cubic logistic models were examined to demonstrate the effectiveness of this method. The accuracy of the designed method was validated by comparing its results with those obtained using the modified Homotopy Perturbation method (MHPM). Error metrics, such as mean absolute error, maximum absolute error, and the experimental convergence rate, are calculated at various collocation points and presented in a tabular format. The findings revealed the method's high accuracy, rapid convergence, and computational efficiency. Overall, the proposed method offers a powerful tool for solving complex differential equations, as evidenced by its strong agreement with MHPM results. The study results were further reinforced through statistical performance metrics and their visual representations, confirming the reliability of the method, low computational cost, and its potential for broad application in numerical computations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101114"},"PeriodicalIF":0.0,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

New existence results on random nonlocal fractional differential equation using approximating sequences

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-05 DOI: 10.1016/j.padiff.2025.101106

Swathi Dhandapani , Ananthi Kantheeban , Karthik Raja Umapathi , Kottakkaran Sooppy Nisar

引用次数: 0

Thermo-fluid dynamics of non-newtonian casson fluid in expanding-contracting channels with joule heating and variable thermal properties

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-05 DOI: 10.1016/j.padiff.2025.101105

Shahid Rafiq , Babar Ahmad Bilal , Aysha Afzal , Jagadish V. Tawade , Nitiraj V. Kulkarni , Barno Abdullaeva , Taoufik Saidani , Manish Gupta

{"title":"Thermo-fluid dynamics of non-newtonian casson fluid in expanding-contracting channels with joule heating and variable thermal properties","authors":"Shahid Rafiq , Babar Ahmad Bilal , Aysha Afzal , Jagadish V. Tawade , Nitiraj V. Kulkarni , Barno Abdullaeva , Taoufik Saidani , Manish Gupta","doi":"10.1016/j.padiff.2025.101105","DOIUrl":"10.1016/j.padiff.2025.101105","url":null,"abstract":"<div><div>This study focuses on the thermo-fluid dynamics of non-Newtonian Casson fluid within a porous channel with expanding and contracting walls, a configuration of significant relevance in industrial applications like cooling systems and biomedical processes such as biofluid transport. The investigation accounts for critical factors such as Joule heating, thermal radiation, porosity, and the temperature dependence of viscosity and thermal conductivity. The governing equations are reduced to ordinary differential equations using similarity transformations and solved with the Least Square Method (LSM). The findings reveal that the Hartmann number and Eckert number strongly influence velocity and temperature profiles. Thermal radiation elevates the core fluid temperature while heat sinks reduce it near the channel walls. Viscosity models demonstrate notable effects on flow resistance and heat transfer. The findings will provide significant applications requiring efficient thermal management and precise control of fluid dynamics, making the results valuable for engineering and biomedical advancements.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101105"},"PeriodicalIF":0.0,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143194090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the solutions of generalized Cauchy differential equations and diffusion equations with k-Hilfer-Prabhakar derivative

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-05 DOI: 10.1016/j.padiff.2025.101119

Ved Prakash Dubey , Jagdev Singh , Sarvesh Dubey , Dumitru Baleanu , Devendra Kumar

引用次数: 0