Solvability for a system of Hadamard-type hybrid fractional differential inclusions

Abstract

In this article, a new system of Hadamard-type hybrid fractional differential inclusions equipped with Dirichlet boundary conditions was constructed. By virtue of a fixed-point theorem due to B. C. Dhage, (Existence results for neutral functional differential inclusions in Banach algebras, Nonlinear Anal. 64 (2006), no. 6, 1290–1306, doi: https://doi.org/10.1016/j.na.2005.06.036), the existence results of solutions for the considered problem are derived in a new norm space for multivalued maps. A numerical example is provided to illustrate our main results.

Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions

“…For more details on Hadamard fractional calculus, we refer the reader to [2][3][4][5][6] and the references therein. In recent years, the study of Hadamard fractional differential equations has attracted the attention of many scholars, mainly focusing on the existence, stability and approximation of solutions (see [7][8][9][10][11][12][13][14][15][16][17][18][19]). For example, Huang et al [9] applied a nonlinear alternative of Leray-Schauder to study the existence of solutions to a nonlinear coupled Hadamard fractional system.…”