Existence of Solutions for Nonlinear Fractional Integro-Differential Equations with Three-Point Nonlocal Fractional Boundary Conditions

Bashir Ahmad,Ahmed Alsaedi

doi:10.1155/2010/691721

Abstract

We prove the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order with three-point nonlocal fractional boundary conditions by applying some standard fixed point theorems.

Highlights

Fractional calculus differentiation and integration of arbitrary order is proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos
A1 There exist positive functions L1 t, L2 t, L3 t such that f t, x t, φx t, ψx t − f t, y t, φy t, ψy t 3.1
This paper studies the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order q ∈ 1, 2 with three-point nonlocal fractional boundary conditions involving the fractional derivative D q−1 /2x ·

Summary

Introduction

Fractional calculus differentiation and integration of arbitrary order is proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos. This branch of calculus has found its applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and image processing, polymer rheology, regular variation in thermodynamics, biophysics, blood flow phenomena, aerodynamics, electro-dynamics of complex medium, viscoelasticity and damping, control theory, wave propagation, percolation, identification, and fitting of experimental data 1–4. Some recent results on nonlocal fractional boundary value problems can be found in 13–15

Preliminaries

Main Results

Conclusions