A fractional system of Cauchy‐reaction diffusion equations by adopting Robotnov function. Issue 3 (16th November 2020)

• Record Type: Journal Article
• Authors: Kumar, Sunil; Ghosh, Surath; Jleli, Mohamed; Araci, Serkan
• Is Part Of: Numerical methods for partial differential equations. Volume 38:Issue 3(2022)
• Page Start: 470
• Page End: 489
• Publication Date: 2020-11-16
• Subjects: generalized DTM -- Robotnov function -- RPSM -- the Cauchy‐reaction diffusion equations -- YAC fractional derivative; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22649
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: This work is motivated essentially by the success of the applications of the nonsingular Yang–Abdel–Aty–Cattani (YAC) derivative in many research area of science, engineering, and financial mathematics. Furthermore, the major determination of this survey work is to achieve Fourier transform of the aforesaid new operator. Obviously, the Cauchy‐reaction diffusion equations have an important role in constructing well‐known models in some fields of science and engineering. Due to this motivation, we applied the aforesaid Robotnov fractional–exponential function‐based new fractional derivative to the Cauchy‐reaction diffusion equations and analyzed the proposed model analytically and graphically by using the generalized differential transform and residual power series methods. Finally, results obtained by the aforesaid proposed methods are found to be in excellent compliance with the known exact solutions. Three numerical examples are considered and described for the accuracy of the results.