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Probl. Anal. Issues Anal., 2020, Volume 9(27), Issue 2, Pages 16–44 (Mi pa294)  

Periodic boundary value problems for fractional implicit differential equations involving Hilfer fractional derivative

M. A. Almalahia, M. S. Abdoab, S. K. Panchala

a Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, (M. S), 431001, India
b Department of Mathematics, Hodiedah University, Al-Hodeidah, Yemen

Abstract: In this paper, a new class of the periodic boundary value problem for nonlinear implicit fractional differential equations involving Hilfer fractional derivative is considered in the weighted space of functions. We establish sufficient conditions for existence, uniqueness, Ulam-Hyers and Ulam-Hyers-Rassias stability of the given problem. The main results are based upon the technique of the Schaefer fixed point theorem, the Banach fixed point theorem, generalized Gronwall inequality, and with the help of some properties of Mittag-Leffler functions. An example is presented to illustrate our main results.

Keywords: fractional differential equations, fractional derivatives, Ulam stability, fixed point theorem, Mittag-Leffler function.

DOI: https://doi.org/10.15393/j3.art.2020.7410

Full text: PDF file (522 kB)
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Bibliographic databases:

UDC: 517.23, 517.9
MSC: 34A08, 34B15, 34A12, 47H10
Received: 19.12.2019
Revised: 25.05.2020
Accepted:27.05.2020
Language:

Citation: M. A. Almalahi, M. S. Abdo, S. K. Panchal, “Periodic boundary value problems for fractional implicit differential equations involving Hilfer fractional derivative”, Probl. Anal. Issues Anal., 9(27):2 (2020), 16–44

Citation in format AMSBIB
\Bibitem{AlmAbdPan20}
\by M.~A.~Almalahi, M.~S.~Abdo, S.~K.~Panchal
\paper Periodic boundary value problems for fractional implicit differential equations involving Hilfer fractional derivative
\jour Probl. Anal. Issues Anal.
\yr 2020
\vol 9(27)
\issue 2
\pages 16--44
\mathnet{http://mi.mathnet.ru/pa294}
\crossref{https://doi.org/10.15393/j3.art.2020.7410}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000541846500002}


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