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

被引：0
|
作者：
Chhetri, Pradeep G. [1 ]
Vatsala, Aghalaya S. [1 ]
机构：
[1] Univ Louisiana Lafayette, Dept Math, Lafayette, LA 70504 USA
来源：
DYNAMIC SYSTEMS AND APPLICATIONS | 2018年 / 27卷 / 04期
关键词：
existence by large; Picard's iterative method; Caputo fractional derivative; fractional reaction diffusion equation;
D O I：
10.12732/dsa.v27i4.10
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 <= q <= 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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页码：837 / 850
页数：14
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