A dynamic competition analysis of stochastic fractional differential equation arising in finance via pseudospectral method

I Ali, SU Khan - Mathematics, 2023 - mdpi.com
This research focuses on the analysis of the competitive model used in the banking sector
based on the stochastic fractional differential equation. For the approximate solution, a …

Spatiotemporal dynamics of reaction–diffusion system and its application to turing pattern formation in a gray–scott model

I Ali, MT Saleem - Mathematics, 2023 - mdpi.com
This paper deals with the effects of partial differential equations on the development of
spatiotemporal patterns in reaction–diffusion systems. These systems describe how the …

Applications of orthogonal polynomials in simulations of mass transfer diffusion equation arising in food engineering

I Ali, MT Saleem - Symmetry, 2023 - mdpi.com
In this paper, Chebyshev polynomials—which are ultraspherical in the first and second kind
and hence symmetric, while the third and fourth order are not ultraspherical and are hence …

A new design and analysis of optimal control problems arising from COVID‐19 outbreak

AIK Butt, DBD Chamaleen, M Imran… - … Methods in the …, 2023 - Wiley Online Library
In this manuscript, we append the hospitalization, diagnosed and isolation compartments to
the classic SEIR model to design a new COVID‐19 epidemic model. We further subdivide …

Special functions and its application in solving two dimensional hyperbolic partial differential equation of telegraph type

I Ali, MT Saleem, A Din - Symmetry, 2023 - mdpi.com
In this article, we use the applications of special functions in the form of Chebyshev
polynomials to find the approximate solution of hyperbolic partial differential equations …

Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation

M Ahmed Alanazi, I Ali - Applied Mathematics in Science and …, 2024 - Taylor & Francis
In this study, we explore the effectiveness of elliptic partial differential equations (PDEs) in
two and three dimensional space based on Helmholtz equation for simulations of acoustic …

Dynamical Analysis of Two-Dimensional Fractional-Order-in-Time Biological Population Model Using Chebyshev Spectral Method

I Ali - Fractal and Fractional, 2024 - mdpi.com
In this study, we investigate the application of fractional calculus to the mathematical
modeling of biological systems, focusing on fractional-order-in-time partial differential …

Discretization and analysis of HIV-1 and HTLV-I coinfection model with latent reservoirs

AM Elaiw, AK Aljahdali, AD Hobiny - Computation, 2023 - mdpi.com
This article formulates and analyzes a discrete-time Human immunodeficiency virus type 1
(HIV-1) and human T-lymphotropic virus type I (HTLV-I) coinfection model with latent …

Editorial for the Special Issue “Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms”

S Sitnik - Mathematics, 2023 - mdpi.com
This Special Issue includes research and survey papers that cover a wide range of topics in
Classical, Computational and Applied Mathematics. High-quality papers on the next wide …

A generalized coupling approach for the weak approximation of stochastic functional differential equations

Y Hamaguchi, D Taguchi - arXiv preprint arXiv:2412.18523, 2024 - arxiv.org
In this paper, we study functional type weak approximation of weak solutions of stochastic
functional differential equations by means of the Euler--Maruyama scheme. Under mild …