Open AccessITERATIVE METHOD APPLIED TO THE FRACTIONAL NONLINEAR SYSTEMS ARISING IN THERMOELASTICITY WITH MITTAG-LEFFLER KERNEL
Author(s) -
Wei Gao,
P. Veeresha,
D. G. Prakasha,
Bilgin Şenel,
Hacı Mehmet Baskonus
Publication year - 2020
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x2040040x
Subject(s) - mathematics , fractional calculus , nonlinear system , uniqueness , laplace transform , kernel (algebra) , order (exchange) , operator (biology) , cauchy distribution , scheme (mathematics) , mathematical analysis , pure mathematics , biochemistry , chemistry , physics , finance , repressor , quantum mechanics , transcription factor , economics , gene
In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is graceful amalgamations of Laplace transform technique with [Formula: see text]-homotopy analysis scheme and fractional derivative defined with Atangana–Baleanu (AB) operator. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the future technique, we consider three different cases and analyzed the projected model in terms of fractional order. Moreover, the physical behavior of the obtained solution has been captured in terms of plots for diverse fractional order, and the numerical simulation is demonstrated to ensure the exactness. The obtained results elucidate that the proposed scheme is easy to implement, highly methodical as well as accurate to analyze the behavior of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.