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

نویسندگان
Slimani, Kamel ID 1
Dob, Sara ID 2
Saadi, Chaima ID 3
Lakhal, Hakim ID 4

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

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

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

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

doi
10.22075/ijnaa.2022.27420.3595
چکیده

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.

کلیدواژه‌ها
Distributional solution, semilinear elliptic system, Leray-Schauder degree, Riesz fractional gradient, homotopy invariance, Partial differential equations