Distributional solution for semilinear system involving fractional gradient and a numerical example

Document Type : Research Paper


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


In this research, a semilinear fractional system involving a new operator is tackled. The existence of a distributional solution is demonstrated and the Leray-Schauder degree method is used to deal with the existence of this system. For the uniqueness of the solution, we use the contraction principle with some assumptions made on the semilinear term $\Phi_{1}$ and $\Phi_{2}$. Then, using an example and the finite difference method a numerical investigation of this system is conducted.


Volume 14, Issue 1
January 2023
Pages 1175-1185
  • Receive Date: 07 June 2022
  • Revise Date: 09 September 2022
  • Accept Date: 21 October 2022