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

 Title EXISTENCE OF THE SOLUTION IN THE LARGE FOR CAPUTO FRACTIONAL REACTION DIFFUSION EQUATION BY PICARD’S METHOD Publication Type Journal Article Year of Publication 2018 Authors CHHETRI PRADEEPG, VATSALA AGHALAYAS Journal Dynamic Systems and Applications Volume 27 Issue 4 Start Page 837 Pagination 14 Date Published 11/2018 ISSN 1056-2176 AMS Subject Classification 34A08, 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. 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