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

	On study the existing result for the time fractional equation using the topological degree method
International Journal of Nonlinear Analysis and Applications
مقاله 2، دوره 16، شماره 1، فروردین 2025، صفحه 11-22 اصل مقاله (506.3 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28891.4017
نویسندگان
Chaima Saadi^* ؛ Hakim Lakhal؛ Kamel Slimani
Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University 20 August 1955 Skikda, Algeria
چکیده
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.
کلیدواژه‌ها
Time fractional derivative؛ Galerkin method؛ Leray-Schauder degree؛ Riemann-Liouville derivative؛ fractional semilinear parabolic equation
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