On Existence and Uniqueness of Solutions of Fractional Integrodifferential Equations with Deviating Arguments under Integral Boundary Conditions

Vinod Vijaykumar Kharat, Anand R. Reshimkar

Abstract

In this paper, we study the existence,uniqueness and boundedness of solutions of following Rieman-Liouville fractional integrodifferential equations with deviating arguments under integral boundary conditions via monotone interative technique by introducing upper and lower solutions:\begin{equation*}\left\{\begin{aligned} D_{0+}^{\alpha} u(t)  & =  f\left(t,u(t),u(\theta(t)),\int_{0}^{t}K(t,s)u(s)ds\right), ~t \in J=[0,T], \\u(0) & =  \lambda \int_{0}^{T}u(s)ds+d,~ d \in \mathbb{R}. \end{aligned} \right.\end{equation*}