# Existence of positive solution to a class of boundary value problems of fractional differential equations

Document Type : Research Paper

Authors

Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan

Abstract

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Thank to classical fixed point theorems of nonlinear alternative of Leray-Schauder and Banach Contraction principle, sufficient conditions are developed under which the proposed problem has at least one solution. An example has been provided to illustrate the main results.

Keywords

### History

• Receive Date: 15 July 2016
• Revise Date: 07 November 2016
• Accept Date: 07 November 2016