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• Open Access

ARTICLE

### On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

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 >

• Open Access

ARTICLE

### Analysis and Numerical Computations of the Multi-Dimensional, Time-Fractional Model of Navier-Stokes Equation with a New Integral Transformation

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3025-3060, 2023, DOI:10.32604/cmes.2023.025470

Abstract The analytical solution of the multi-dimensional, time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transform decomposition method is presented in this article. The aforesaid model is analyzed by employing Caputo fractional derivative. We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods, respectively. The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems. The exact and estimated solutions are delineated via numerical simulation. The proposed analysis indicates that the projected configuration is extremely meticulous, highly efficient, and precise in understanding the behavior… More >

• Open Access

ARTICLE

### Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1931-1950, 2023, DOI:10.32604/cmes.2023.025033

Abstract In this work, we present a model that uses the fractional order Caputo derivative for the novel Coronavirus disease 2019 (COVID-19) with different hospitalization strategies for severe and mild cases and incorporate an awareness program. We generalize the SEIR model of the spread of COVID-19 with a private focus on the transmissibility of people who are aware of the disease and follow preventative health measures and people who are ignorant of the disease and do not follow preventive health measures. Moreover, individuals with severe, mild symptoms and asymptomatically infected are also considered. The basic reproduction number () and local stability… More >

• Open Access

ARTICLE

### The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 259-273, 2023, DOI:10.32604/cmes.2022.021332

Abstract In the last few decades, it has become increasingly clear that fractional calculus always plays a very significant role in various branches of applied sciences. For this reason, fractional partial differential equations (FPDEs) are of more importance to model the different physical processes in nature more accurately. Therefore, the analytical or numerical solutions to these problems are taken into serious consideration and several techniques or algorithms have been developed for their solution. In the current work, the idea of fractional calculus has been used, and fractional Fornberg Whitham equation (FFWE) is represented in its fractional view analysis. A well-known method… More >

• Open Access

ARTICLE

### Optimal and Memristor-Based Control of A Nonlinear Fractional Tumor-Immune Model

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 3463-3486, 2021, DOI:10.32604/cmc.2021.015161

Abstract In this article, the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune. The fractional derivatives are described in the Caputo sense. The solutions derived using this method are easy and very accurate. The model is given by its signal flow diagram. Moreover, a simulation of the system by the Simulink of MATLAB is given. The disease-free equilibrium and stability of the equilibrium point are calculated. Formulation of a fractional optimal control for the cancer model is calculated. In addition, to control the system, we propose a novel modification of its model. This modification is… More >

• Open Access

ARTICLE

### The Efficient Finite Element Methods for Time-Fractional Oldroyd-B Fluid Model Involving Two Caputo Derivatives

CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.1, pp. 173-195, 2020, DOI:10.32604/cmes.2020.011871

Abstract In this paper, we consider the numerical schemes for a timefractional Oldroyd-B fluid model involving the Caputo derivative. We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes. Numerical examples for two-dimensional problems further confirm the robustness of the schemes with first- and second-order accurate in time. More >

• Open Access

ARTICLE

### A Discrete Model of TB Dynamics in Khyber Pakhtunkhwa-Pakistan

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 777-795, 2020, DOI:10.32604/cmes.2020.08208

Abstract The present paper investigates the theoretical analysis of the tuberculosis (TB) model in the discrete-time case. The model is parameterized by the TB infection cases in the Pakistani province of Khyber Pakhtunkhwa between 2002 and 2017. The model is parameterized and the basic reproduction number is obtained and it is found R0 ¼ 1:5853. The stability analysis for the model is presented and it is shown that the discrete-time tuberculosis model is stable at the disease-free equilibrium whenever R0 < 1 and further we establish the results for the endemic equilibria and prove that the model is globally asymptotically stable… More >

• Open Access

ARTICLE

### Fractional Analysis of Viscous Fluid Flow with Heat and Mass Transfer Over a Flexible Rotating Disk

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.1, pp. 377-400, 2020, DOI:10.32604/cmes.2020.08076

Abstract An unsteady viscous fluid flow with Dufour and Soret effect, which results in heat and mass transfer due to upward and downward motion of flexible rotating disk, has been studied. The upward or downward motion of non rotating disk results in two dimensional flow, while the vertical action and rotation of the disk results in three dimensional flow. By using an appropriate transformation the governing equations are transformed into the system of ordinary differential equations. The system of ordinary differential equations is further converted into first order differential equation by selecting suitable variables. Then, we generalize the model by using… More >

• Open Access

ARTICLE

### A Jacobi Spectral Collocation Scheme Based on Operational Matrix for Time-fractional Modified Korteweg-de Vries Equations

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.3, pp. 185-209, 2015, DOI:10.3970/cmes.2015.104.185

Abstract In this paper, a high accurate numerical approach is investigated for solving the time-fractional linear and nonlinear Korteweg-de Vries (KdV) equations. These equations are the most appropriate and desirable definition for physical modeling. The spectral collocation method and the operational matrix of fractional derivatives are used together with the help of the Gauss-quadrature formula in order to reduce such problem into a problem consists of solving a system of algebraic equations which greatly simplifying the problem. Our approach is based on the shifted Jacobi polynomials and the fractional derivative is described in the sense of Caputo. In addition, the presented… More >

• Open Access

ARTICLE

### Variational Iteration Method for the Time-Fractional Elastodynamics of 3D Quasicrystals

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.1, pp. 29-38, 2012, DOI:10.3970/cmes.2012.086.029

Abstract This paper presents the approximate analytical solutions to the time fractional differential equations of elasticity for 3D quasicrystals with initial conditions. These equations are written in the form of a vector partial differential equation of the second order. The time fractional vector partial differential equations with initial conditions are solved by variational iteration method (VIM). The fractional derivatives are described in the Caputo sense. Numerical example shows that the proposed method is quite effective and convenient for solving kinds of time fractional system of partial differential equations. More >

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