Existence and uniqueness of solutions for Caputo-Hadamard sequential fractional order neutral functional differential equations. (English) Zbl 1360.34159

Ahmad, Bashir; Ntouyas, Sotiris K.

Electron. J. Differ. Equ. 2017, Paper No. 36, 11 p. (2017).

Summary: 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.

MSC:

34K37	Functional-differential equations with fractional derivatives
34K40	Neutral functional-differential equations
47N20	Applications of operator theory to differential and integral equations

Keywords:

fractional differential equations; existence; fixed point; functional fractional differential equations; Caputo-Hadamard fractional differential equations