Abstract
In this manuscript, we talk over the existence of solutions of a class of hybrid Caputo–Hadamard fractional differential inclusions with Dirichlet boundary conditions. Our results are based on the Arzelá–Ascoli theorem and some suitable theorems of fixed point theory. As well, to illustrate our results, we confront the exceptional case of the fractional differential inclusions with examples.
Highlights
During the last decade, the subject of fractional differential equations and inclusions has been developed intensively
Hybrid fractional differential equations and inclusions, certain classes of equations and inclusions involve the fractional derivative of an unknown function hybrid with the nonlinearity depending on it
Most of the workplace on the fractional differential equations and inclusions is based on Riemann–Liouville, Caputo, and Hadamard type fractional derivatives
Summary
The subject of fractional differential equations and inclusions has been developed intensively (for example, see [1,2,3,4,5,6,7,8] and the references therein). Hybrid fractional differential equations and inclusions, certain classes of equations and inclusions involve the fractional derivative of an unknown function hybrid with the nonlinearity depending on it. They have been examined by several researchers (for example, see [13,14,15]). M, μ : C(J, R) → R, and the multifunction G : J × R → P(R) satisfies certain conditions (for more details, see [14]) Motivated by these articles, we look into the existence of solutions for the following hybrid Caputo–Hadamard fractional differential inclusion:
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