Existence results for neutral functional fractional differential equations with state dependent-delay

Velusamy Kavithaa,*,  Peng-Zhen Wangb and R. Murugesuc

Existence results for neutral functional fractional differential equations with state dependent-delay

Authors :

Velusamy Kavitha^a,*, Peng-Zhen Wang^b and R. Murugesu^c

Author Address :

^aDepartment of Mathematics, Karunya University, Karunya Nagar, Coimbatore-641 114, Tamil Nadu, Inda.
^bDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou-730070, China.
^cDepartment of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts & Science, Coimbatore-641 020, India.

*Corresponding author.

Abstract :

In this paper, we provide sufficient conditions for the existence of mild solutions for a class of fractional differential equations with state-dependent delay. The results are obtained by using the nonlinear alternative of Leray-Schauder type [14] fixed point theorem. An example is provided to illustrate the main results.

Keywords :

Functional differential equation, fractional derivative, fractional integral, state-dependent delay, fixed point.

DOI :

Article Info :

Received : September 12, 2012; Accepted : September 25, 2012.