Saima Rashid^1,2,*, Fahd Jarad^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 2289-2327, 2024, DOI:10.32604/cmes.2023.028773

Abstract Because of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic element in every cohort and… More >

Rania Saadeh¹, Ahmad Qazza¹, Aliaa Burqan¹, Shrideh Al-Omari^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3121-3139, 2023, DOI:10.32604/cmes.2023.026313

Abstract This paper aims to investigate a new efficient method for solving time fractional partial differential equations. In this orientation, a reliable formable transform decomposition method has been designed and developed, which is a novel combination of the formable integral transform and the decomposition method. Basically, certain accurate solutions for time-fractional partial differential equations have been presented. The method under concern demands more simple calculations and fewer efforts compared to the existing methods. Besides, the posed formable transform decomposition method has been utilized to yield a series solution for given fractional partial differential equations. Moreover, several interesting formulas relevant to the… More >

Kamran¹, Siraj Ahmad¹, Kamal Shah^2,3,*, Thabet Abdeljawad^2,4,*, Bahaaeldin Abdalla²

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2743-2765, 2023, DOI:10.32604/cmes.2023.023705

Abstract Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects. Using the Laplace transform for solving differential equations, however, sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analytical means. Thus, we need numerical inversion methods to convert the obtained solution from Laplace domain to a real domain. In this paper, we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with order . Our proposed numerical scheme is based on… More > Graphic Abstract

Nawab Hussain^1,*, Saud M. Alsulami¹, Hind Alamri^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2617-2648, 2023, DOI:10.32604/cmes.2023.023143

Abstract In this paper, we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces. Furthermore, we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated with and consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations. We also establish certain interesting examples to illustrate the usability of our results. More >

Mustafa Turkyilmazoglu^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 47-65, 2022, DOI:10.32604/cmes.2022.020781

Abstract An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) is modified via introducing a functional term involving both a variable and a parameter. A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L² norm. Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate, more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus of mathematical models. Better… More >

Mahmoud H. Taha¹, Mohamed A. Ramadan^2,*, Dumitru Baleanu^3,4,5, Galal M. Moatimid¹

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 969-983, 2020, DOI:10.32604/cmes.2020.010942

Abstract The current paper is concerned with a modified Homotopy perturbation technique. This modification allows achieving an exact solution of an initial value problem of the fractional differential equation. The approach is powerful, effective, and promising in analyzing some classes of fractional differential equations for heat conduction problems and other dynamical systems. To crystallize the new approach, some illustrated examples are introduced. More >

Farnaz Ismail¹, Mubashir Qayyum^{2, *}, Syed Inayat Ali Shah¹

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 825-845, 2020, DOI:10.32604/cmes.2020.011073

Abstract Modeling and analysis of thin film flow with respect to magneto hydro dynamical effect has been an important theme in the field of fluid dynamics, due to its vast industrial applications. The analysis involves studying the behavior and response of governing equations on the basis of various parameters such as thickness of the film, film surface profile, shear stress, liquid velocity, volumetric flux, vorticity, gravity, viscosity among others, along with different boundary conditions. In this article, we extend this analysis in fractional space using a homotopy based scheme, considering the case of a Non-Newtonian Pseudo-Plastic fluid for lifting and drainage… More >

Yanxin Wang^{1, *}, Li Zhu¹, Zhi Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.2, pp. 339-350, 2019, DOI:10.31614/cmes.2019.04575

Abstract An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper. The properties of Euler wavelets and their operational matrix together with a family of piecewise functions are first presented. Then they are utilized to reduce the problem to the solution of a nonlinear system of algebraic equations. And the convergence of the Euler wavelets basis is given. The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy. More >

Yiming Chen¹, Xiaoning Han¹, Lechun Liu ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.5, pp. 391-405, 2014, DOI:10.3970/cmes.2014.097.391

Abstract In this paper, a class of linear system of fractional differential equations is considered. It has been solved by operational matrix of Haar wavelet method which converts the problem into algebraic equations. Moreover the convergence of the method is studied, and three numerical examples are provided to demonstrate the accuracy and efficiency. More >

Xiaomin Wang^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.2, pp. 169-182, 2014, DOI:10.3970/cmes.2014.102.169

Abstract In this paper, an efficient and robust wavelet Laplace inversion method of solving the fractional differential equations is proposed. Such an inverse function can be applied to any reasonable function categories and it is not necessary to know the properties of original function in advance. As an example, we have applied the proposed method to the solution of the Bagley–Torvik equations and Numerical examples are given to demonstrate the efficiency and accuracy of the proposed. More >