On study the existing result for the time fractional equation using the topological degree method

Document Type : Research Paper

Authors

Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University 20 August 1955 Skikda, Algeria

10.22075/ijnaa.2023.28891.4017

Abstract

In this article, we suggest introducing the Riemann-Liouville time fractional derivative to a fractional equation (FPDE) involving a fractional Laplacian. Our work is divided into two parts. In the first part, the existence and uniqueness of time fractional linear equations are demonstrated, and the Galerkin approach is proposed to deal with them. In the second part, we investigate the existence results of the time fractional semilinear equation. To solve This problem, the Leray-Schauder degree method has been used with some conditions on the semilinear term.

Keywords

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Articles in Press, Corrected Proof
Available Online from 31 January 2024
  • Receive Date: 04 November 2022
  • Accept Date: 16 December 2023