A new compact alternating direction implicit method for solving two dimensional time fractional diffusion equation with Caputo-Fabrizio derivative

Taghipour, M.; Aminikhah, Hossein

doi:10.2298/fil2011609t

Cited by 7 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, extensive studies [17][18][19] have been conducted on the mathematical analysis of fractional derivatives and integrals. The fractional-order derivative is nonlocal and includes the historical and long-term memory effect of the system, and this is one of its most important advantages over the integer-order derivative, which helps to model natural phenomena better [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

Mohammadi

Kaabar

Alzabut

et al. 2021

Journal of Function Spaces

View full text Add to dashboard Cite

Crimean-Congo hemorrhagic fever is a common disease between humans and animals that is transmitted to humans through infected ticks, contact with infected animals, and infected humans. In this paper, we present a boxed model for the transmission of Crimean-Congo fever virus. With the help of the fixed-point theory, our proposed system model is investigated in detail to prove its unique solution. Given that the Caputo fractional-order derivative preserves the system’s historical memory, we use this fractional derivative in our modeling. The equilibrium points of the proposed system and their stability conditions are determined. Using the Euler method for the Caputo fractional-order derivative, we calculate the approximate solutions of the fractional system, and then, we present a numerical simulation for the transmission of Crimean-Congo hemorrhagic fever.

show abstract

Section: Introductionmentioning

confidence: 99%

A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

Mohammadi

Kaabar

Alzabut

et al. 2021

Journal of Function Spaces

View full text Add to dashboard Cite

show abstract

“…In this section, we provide two examples to illustrate efficiency of schemes (39) and (40). All experiments are performed on a Windows 10 (64 bit) Intel(R) Core(TM) i7-7500U CPU 2.70 GHz, 8.0 GB of RAM using MATLAB R2017b.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…A discrete approximation to the CF 0 D c t u(x, t) at (x j , t k ) can be obtained by the following approximation [40]:…”

Section: Numerical Schemementioning

confidence: 99%

A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative

Taghipour

Aminikhah

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of the coupled Burgers equations with the Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have been approximated by first and second derivatives of the cubic B-spline quasi-interpolation. The discrete scheme obtained in this way constitutes a system of algebraic equations associated with a bi-pentadiagonal matrix. We show that the proposed scheme is unconditionally stable. Numerical examples are provided to verify the efficiency of the method.

show abstract

“…Semary et al [7] approximated the solution of Liouville-Caputo VO FPDEs with 0 < α(t) ≤ 1 based on the Chebyshev function and discussed many linear and non-linear non-integer-order PDEs. Taghipour and Aminikhah [8] proposed the ADI numerical scheme for the fractional-order model and discussed the theoretical analysis. Other related studies can be seen in [9][10][11][12][13][14][15][16].…”

mentioning

confidence: 99%

An investigation of a closed-form solution for non-linear variable-order fractional evolution equations via the fractional Caputo derivative

Ali

Alahmadi²,

Abdullah³

et al. 2023

Front. Phys.

View full text Add to dashboard Cite

Determining the non-linear traveling or soliton wave solutions for variable-order fractional evolution equations (VO-FEEs) is very challenging and important tasks in recent research fields. This study aims to discuss the non-linear space–time variable-order fractional shallow water wave equation that represents non-linear dispersive waves in the shallow water channel by using the Khater method in the Caputo fractional derivative (CFD) sense. The transformation equation can be used to get the non-linear integer-order ordinary differential equation (ODE) from the proposed equation. Also, new exact solutions as kink- and periodic-type solutions for non-linear space–time variable-order fractional shallow water wave equations were constructed. This confirms that the non-linear fractional variable-order evolution equations are natural and very attractive in mathematical physics.

show abstract

A new compact alternating direction implicit method for solving two dimensional time fractional diffusion equation with Caputo-Fabrizio derivative

Cited by 7 publications

References 19 publications

A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative

An investigation of a closed-form solution for non-linear variable-order fractional evolution equations via the fractional Caputo derivative

Contact Info

Product

Resources

About