Hilfer and Hilfer-Hadamard Fractional Differential Equations with Random Effects

Said Abbas, Mouffak Benchohra, Naima Hamidi

Abstract


This paper deals with some existence and Ulam stability results for some
functional differential equations of Hilfer and Hilfer-Hadamard type. An application is made of Itoh's random fixed point theorem for the existence of random solutions. Next we prove that our problems are generalized Ulam-Hyers-Rassias stable.

Keywords


Functional Random differential equation; mixed Riemann-Liouville integral of fractional order; mixed Hadamard integral of fractional order; Hilfer fractional derivative; Hilfer-Hadamard fractional derivative; existence; Ulam stability

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DOI: http://dx.doi.org/10.14510%2Flm-ns.v37i1.1378