Open AccessGeneralized Monotone Method for Caputo Fractional Reaction-Diffusion Equation
Author(s) -
Vaibhav B. Jagzap
Publication year - 2022
Publication title -
international journal of advanced research in science, communication and technology
Language(s) - English
Resource type - Journals
ISSN - 2581-9429
DOI - 10.48175/ijarsct-3088
Subject(s) - monotone polygon , monotonic function , mathematics , reaction–diffusion system , diffusion , diffusion equation , mathematical analysis , function (biology) , representation (politics) , physics , thermodynamics , geometry , economy , evolutionary biology , biology , politics , political science , law , economics , service (business)
In this paper, our aim is to obtain the integral representation for the solution of non-linear Caputo reaction-diffusion equation of order q, where 0 < q < 1, in term of Green’s function. We have developed a generalized monotone method for non-linear weakly coupled Caputo reaction-diffusion equation. The generalized monotone method yields monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. The existence of a unique solution for the non-linear Caputo reaction-diffusion equation is obtained.