Anil Kumar
Fractional differential equations (FDEs) are a more advanced version of classical equations that consist of non-integer order derivatives. This modification of differential equations allows modeling complex systems with memory effects,...
Fractional differential equations
Memory effects
Grünwald–Letnikov derivative
Numerical methods
Open Access
June 30, 2026
Pappu Verma
,
Sachin Kumar
In this study, we introduce an efficient numerical approach for solving time-fractional differential equations that use the Atangana-Baleanu fractional derivative with the Mittag-Leffler kernel. We showcase the applicability of the...
Keller-Segel equations
Fractional PDE
Mittag-Leffler kernel fractional derivative
Spectral method
Open Access
June 30, 2026
Madhubala Madhubala
,
Sachin Kumar
In this article, we study a new type of mathematical model of the diffusion equation. This model has space and time-fractional derivative with both singular and non-singular derivative i.e., having power-law kernel and Mittag-Leffler...
Fractional PDE
Fuzzy valued function
diffusion equation
time delay
Chebyshev polynomial
Open Access
June 30, 2026
Prashant Pandey
,
Suraj Prasad
,
Priya Kumari
In the present scientific article, an efficient operational matrix based on the famous Bernstein polynomials is applied for the numerical solution of two-dimensional non-linear variable order reaction-diffusion equation in porous media...
Fractional calculus
Variable order derivative
Sub-diffusion
Porous Media
Stability and Convergence Analysis
Open Access
June 30, 2026
Pavitra Dhanda
,
Prashant Pandey
This article presents a Laguerre-Galerkin approximation for the numerical solution of time-fractional sub-diffusion equations involving the Caputo fractional derivative. The proposed methodology employs the separation of variables...
Time-fractional Sub-Diffusion
Galerkin Method
Mittag-Leffler function
Laguerre polynomial
Open Access
June 30, 2026
Anil Kumar
This study examines the HU-stability of a class of fractional functional differential systems including the “Caputo–Fabrizio derivative”, which is especially efficient in modelling systems with non-immediate impulses due of its...
Caputo–Fabrizio fractional derivative
stability analysis
HU-stability
Open Access
June 30, 2026
