Existence and uniqueness results for positive solutions of Hadamard type fractional BVP

Abstract

In this paper, we investigate the existence and multiplicity results of positive solutions for a fractional boundary value problem associated with integral boundary condition via Hadamard Fractional operator. We first derive Green¢s function associated with the BVP and prove its properties. The results for existence and uniqueness of solutions are derived by applying two fixed point theorems of a sum operator in partial ordering Banach space. The main results obtained can not only guarantee the existence of a unique positive solution, but also be applied to construct an iterative scheme for approximating it.

Subject Classification: (2010):

• Primary 26A33
• Secondary 34B15

Keywords:

• Hadamard fractional derivative
• Fractional boundary value problem
• Fixed point theorem
• Integral boundary conditions