Premium
An analytic study on the approximate solution of a nonlinear time‐fractional Cauchy reaction–diffusion equation with the Mittag–Leffler law
Author(s) -
Hosseini Kamyar,
Ilie Mousa,
Mirzazadeh Mohammad,
Baleanu Dumitru
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7059
Subject(s) - mathematics , uniqueness , laplace transform , fractional calculus , cauchy distribution , mathematical analysis , cauchy problem , nonlinear system , initial value problem , homotopy analysis method , fixed point theorem , homotopy , pure mathematics , physics , quantum mechanics
The main aim of the current article is considering a nonlinear time‐fractional Cauchy reaction–diffusion equation with the Mittag–Leffler law and deriving its approximate analytical solution in a systematic way. More precisely, after reformulating the nonlinear time‐fractional Cauchy reaction–diffusion equation with the Mittag–Leffler law, its approximate analytical solution is derived formally through the use of the homotopy analysis transform method (HATM) which is based on the homotopy method and the Laplace transform. The existence and uniqueness of the solution of the nonlinear time‐fractional Cauchy reaction–diffusion equation with the Mittag–Leffler law are also studied by adopting the fixed‐point theorem. In the end, by considering some two‐ and three‐dimensional graphs, the influence of the order of time‐fractional operator on the displacement is examined in detail.