EXISTENCE OF THE SOLUTION IN THE LARGE FOR CAPUTO FRACTIONAL REACTION DIFFUSION EQUATION BY PICARD’S METHOD

TitleEXISTENCE OF THE SOLUTION IN THE LARGE FOR CAPUTO FRACTIONAL REACTION DIFFUSION EQUATION BY PICARD’S METHOD
Publication TypeJournal Article
Year of Publication2018
AuthorsCHHETRI PRADEEPG, VATSALA AGHALAYAS
JournalDynamic Systems and Applications
Volume27
Issue4
Start Page837
Pagination14
Date Published11/2018
ISSN1056-2176
AMS Subject Classification34A08, 34R11
Abstract

In this work, we have developed Picard's iterative method to prove the existence and uniqueness of the solution of the nonlinear Caputo fractional reaction diffusion equation in one dimensional space. The order of the fractional time derivative q is such that $0.5\leq q\leq 1$. The existence result has been proved by a priori assuming the solution is bounded. Thus, we refer to this method as existence of solution in the large. The method can be  extended to the Caputo fractional reaction diffusion system also.

PDFhttps://acadsol.eu/dsa/articles/27/4/10.pdf
DOI10.12732/dsa.v27i4.10
Refereed DesignationRefereed
Full Text

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