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 J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 5, Pages 535–549 (Mi jsfu696)

Weighted fractional neutral functional differential equations

Mohammed S. Abdoab, Satish K. Panchala

a Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431 004 (M.S.), India
b Department of Mathematics, Hodeidah University, Al-Hodeidah-3114, Yemen

Abstract: In this paper, we consider a weighted neutral functional differential equation of fractional order $0<\alpha <1$, with nonzero initial values, infinite delay, and the standard Riemann–Liouville fractional derivative. By using a variety of tools of fractional calculus including the Schauder fixed point theorem and the Banach fixed point theorem, we verify the existence, uniqueness and continuous dependence of solution of weighted neutral problem.

Keywords: fractional functional differential equations, fractional derivative and fractional integral, existence and continuous dependence, fixed point theorem.

DOI: https://doi.org/10.17516/1997-1397-2018-11-5-535-549

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UDC: 517.9
Accepted: 16.07.2018
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Citation: Mohammed S. Abdo, Satish K. Panchal, “Weighted fractional neutral functional differential equations”, J. Sib. Fed. Univ. Math. Phys., 11:5 (2018), 535–549

Citation in format AMSBIB
\Bibitem{AbdPan18} \by Mohammed~S.~Abdo, Satish~K.~Panchal \paper Weighted fractional neutral functional differential equations \jour J. Sib. Fed. Univ. Math. Phys. \yr 2018 \vol 11 \issue 5 \pages 535--549 \mathnet{http://mi.mathnet.ru/jsfu696} \crossref{https://doi.org/10.17516/1997-1397-2018-11-5-535-549} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000447374900001} 

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This publication is cited in the following articles:
1. Abdo M.S., Wahash H.A., Panchal S.K., “Positive Solution of a Fractional Differential Equation With Integral Boundary Conditions”, J. Appl. Math. Comput. Mech., 17:3 (2018), 5–15
2. Ufa Math. J., 11:4 (2019), 151–170
3. M. S. Abdo, S. K. Panchal, A. M. Saeed, “Fractional boundary value problem with psi-Caputo fractional derivative”, Proc. Indian Acad. Sci.-Math. Sci., 129:5 (2019), UNSP 65
4. H. A. Wahash, M. S. Abdo, S. K. Panchal, “An existence result for fractional integro-differential equations in Banach spaces”, J. Math. Ext., 13:3 (2019), 19–33
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