Work

Analytical and Numerical Treatment of Evolutionary Time-Fractional Partial Integro-Differential Equations with Singular Memory Kernels

Year: 2025

Type: article

Abstract: Evolution equations with fractional-time derivatives and singular memory kernels are used for modeling phenomena exhibiting hereditary properties, as they effectively incorporate memory effects into their formulation. Time-fractional partial integro-differential equations (FPIDEs) represent a significant class of such evolution equations and are widely used in diverse scientific and engineering fields. In this study, we use the sinc-collocation and iterative Laplace transform methods to solve a specific FPIDE with a weakly singular kernel. Specifically, the sinc-collocation method is applied to discretize the spatial domain, while a combination of numerical techniques is utilized for temporal discretization. Then, we prove the convergence analytically. To compare the two methods, we provide two examples. We notice that both the sinc-collocation and iterative Laplace transform methods provide good approximations. Moreover, we find that the accuracy of the methods is influenced by fractional order α∈(0,1) and the memory-kernel parameter β∈(0,1). We observe that the error decreases as β increases, where the kernel becomes milder, which extends the single-value study of β=1/2 in the literature.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9060392

Authors: Kamel Al-Khaled, Isam Al-Darabsah, Amer Darweesh, Amro Alshare

Institution: Jordan University of Science and Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Jordan University of Science and Technology