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Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative. (English) Zbl 1442.34017

Summary: In this paper, the existence, uniqueness and stability of random implicit fractional differential equations (RIFDs) with nonlocal condition and impulsive effect involving a generalized Hilfer fractional derivative (HFD) are discussed. The arguments are discussed via Krasnoselskii’s fixed point theorems, Schaefer’s fixed point theorems, Banach contraction principle and Ulam type stability. Some examples are included to ensure the abstract results.

MSC:

34A08 Fractional ordinary differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
34F05 Ordinary differential equations and systems with randomness
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34A37 Ordinary differential equations with impulses
47N20 Applications of operator theory to differential and integral equations
34D10 Perturbations of ordinary differential equations
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