Abstract
This paper deals with some existence results in Banach spaces for Hilfer and Hilfer-Hadamard fractional differential inclusions. The main tools used in the proofs are Monch's fixed point theorem and the concept of a measure of noncompactness.
Highlights
Fractional differential equations and inclusions appear in several areas such as engineering, mathematics, bio-engineering, physics, and other applied sciences [19, 32]
For some fundamental results in the theory of fractional calculus and fractional differential equations, we refer the reader to the monographs of Abbas et al [4, 5], Kilbas et al [23], Samko et al [31], Zhou [35], as well as the papers by Abbas et al [1, 2], Benchohra et al [10], Lakshmikantham et al [24, 25, 26] and the references therein
Considerable attention has been given to the existence of solutions of initial and boundary value problems for fractional differential equations with Hilfer fractional derivative; see [14, 15, 19, 21, 33, 34] and the references therein
Summary
Fractional differential equations and inclusions appear in several areas such as engineering, mathematics, bio-engineering, physics, and other applied sciences [19, 32]. In [3, 8, 9, 11, 12, 16, 17] the authors applied the measure of noncompactness to some classes of Riemann-Liouville or Caputo fractional differential equations in Banach spaces. By L1(I), we denote the space of measurable functions v : I → E that are Bochner integrable and normed by v(t) dt.
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