A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions

Bashir Ahmad,Sotiris K Ntouyas,Ahmed Alsaedi

doi:10.1155/2013/320415

Abstract

We develop the existence theory for nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type boundary conditions involving nonintersecting finite many strips of arbitrary length. Our results are based on some standard tools of fixed point theory. For the illustration of the results, some examples are also discussed.

Highlights

The subject of fractional calculus has recently developed into a hot topic for the researchers in view of its numerous applications in the field of physics, mechanics, chemistry, engineering, and so forth
Let C := C([0, T], R) denotes the Banach space of all continuous functions defined on [0, T] × R endowed with a topology of uniform convergence with the norm ‖x‖ = supt∈[0,T]|x(t)|
In the first result we prove an existence and uniqueness result by means of Banach’s contraction mapping principle

Summary

Introduction

The subject of fractional calculus has recently developed into a hot topic for the researchers in view of its numerous applications in the field of physics, mechanics, chemistry, engineering, and so forth. The boundary value problem (1) has a unique solution provided where Λ is given by (14). Let us consider the following 4-strip nonlocal boundary value problem: cD9/2x (t) = f (t, x (t)) , t ∈ [0, 2] , x (0) = 0, x󸀠 (0) = 0, x󸀠󸀠 (0) = 0, x󸀠󸀠󸀠 (0) = 0, x (T) = ∑γi [Iβix (ηi) − Iβix (ζi)] , i=1 (19)

Objectives

Results

Conclusion