Analysis of differential equations involving Caputo–Fabrizio fractional operator and its applications to reaction–diffusion equations

Advances in Difference Equations

Asifa Tassaddiq¹  Amjad Shaikh²  Dumitru Baleanu³  Kottakkaran Sooppy Nisar⁴ 

[1] College of Computer and Information Sciences, Majmaah University;Department of Mathematics, AKI’s Poona College of Arts, Science and Commerce;Department of Mathematics, Cankaya University;Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University;

关键词: Caputo–Fabrizio derivative operator;    Existence and uniqueness;    Fixed point theorem;    Iterative Laplace transform method;    Approximate solutions;   

DOI  :  10.1186/s13662-019-2115-3

来源: DOAJ

【 摘 要 】

Abstract This manuscript deals with fractional differential equations including Caputo–Fabrizio differential operator. The conditions for existence and uniqueness of solutions of fractional initial value problems is established using fixed point theorem and contraction principle, respectively. As an application, the iterative Laplace transform method (ILTM) is used to get an approximate solutions for nonlinear fractional reaction–diffusion equations, namely the Fitzhugh–Nagumo equation and the Fisher equation in the Caputo–Fabrizio sense. The obtained approximate solutions are compared with other available solutions from existing methods by using graphical representations and numerical computations. The results reveal that the proposed method is most suitable in terms of computational cost efficiency, and accuracy which can be applied to find solutions of nonlinear fractional reaction–diffusion equations.

【 授权许可】

Unknown