Electron. J. Differential Equations, Vol. 2017 (2017), No. 36, pp. 1-11.

Existence and uniqueness of solutions for Caputo-Hadamard sequential fractional order neutral functional differential equations

Bashir Ahmad, Sotiris K. Ntouyas

In this article, we study the existence and uniqueness of solutions for Hadamard-type sequential fractional order neutral functional differential equations. The Banach fixed point theorem, a nonlinear alternative of Leray-Schauder type and Krasnoselski fixed point theorem are used to obtain the desired results. Examples illustrating the main results are presented. An initial value integral condition case is also discussed.

Submitted November 11, 2016. Published February 2, 2017.
Math Subject Classifications: 34A08, 34K05.
Key Words: Fractional differential equations; existence; fixed point; functional fractional differential equations; Caputo-Hadamard fractional differential equations.

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Bashir Ahmad
Department of Mathematics
Faculty of Science
King Abdulaziz University P.O. Box. 80203
Jeddah 21589, Saudi Arabia
email: bashirahmad_qau@yahoo.com
Sotiris K. Ntouyas
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: sntouyas@uoi.gr

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