Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682214120230101Distributional solution for semilinear system involving fractional gradient and a numerical example11751185710110.22075/ijnaa.2022.27420.3595ENChaimaSaadiLaboratory of Applied Mathematics and History and Didactics of mathematics (LAMAHIS), University 20 August 1955 Skikda, Algeria0000-0003-4944-1846HakimLakhalLaboratory of Applied Mathematics and History and Didactics of mathematics (LAMAHIS), University 20 August 1955 Skikda, Algeria0000-0003-1066-0216KamelSlimaniLaboratory of Applied Mathematics and History and Didactics of mathematics (LAMAHIS), University 20 August 1955 Skikda, Algeria0000-0001-8404-8148SaraDobLaboratory of Applied Mathematics and History and Didactics of mathematics (LAMAHIS), University 20 August 1955 Skikda, AlgeriaJournal Article20220607In 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.https://ijnaa.semnan.ac.ir/article_7101_ed8c276a1371bf2efdbb59269ea8cf8a.pdf