In this work, we have developed Picard{\textquoteright}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.

}, keywords = {34A08, 34R11}, issn = {1056-2176}, doi = {10.12732/dsa.v27i4.10}, url = {https://acadsol.eu/dsa/articles/27/4/10.pdf}, author = {PRADEEP G. CHHETRI and AGHALAYA S. VATSALA} }