Initial value problems of fractional order Hadamard-type functional differential equations. (English) Zbl 1320.34109

Ahmad, Bashir; Ntouyas, Sotiris K.

Electron. J. Differ. Equ. 2015, Paper No. 77, 9 p. (2015).

The authors investigate the existence and uniqueness of solutions for fractional order Hadamard-type functional and neutral functional differential equations by using the Banach fixed point theorem and a nonlinear alternative of Leray-Schauder type. An example is provided to illustrate the theory.

Reviewer: Krishnan Balachandran (Coimbatore)

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 equation; functional differential equation; Hadamard fractional differential equation; existence of solutions; fixed point