Abstract
In this paper, we discuss the existence and uniqueness of solutions for a Riemann-Liouville type fractional differential equation with nonlocal four-point Riemann-Liouville fractional-integral boundary conditions by means of classical fixed point theorems. An illustration of main results is also presented with the aid of some examples. MSC:34A08, 34B10, 34B15.
Highlights
1 Introduction In recent years, boundary value problems of nonlinear fractional differential equations with a variety of boundary conditions have been investigated by many researchers
As a matter of fact, fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. This is one of the characteristics of fractional-order differential operators that contributes to the popularity of the subject and has motivated many researchers and modelers to shift their focus from classical models to fractional order models
There has been a significant progress in the theoretical analysis like periodicity, asymptotic behavior and numerical methods for fractional differential equations
Summary
Boundary value problems of nonlinear fractional differential equations with a variety of boundary conditions have been investigated by many researchers. In [ ], the authors recently studied a problem of Riemann-Liouville fractional differential equations with fractional boundary conditions: Dαu(t) = f t, u(t) , t ∈ [ , T], α ∈ In this paper, motivated by [ ], we study a fully Riemann-Liouville fractional nonlocal integral boundary value problem given by. Where Dα denotes the Riemann-Liouville fractional derivative of order α, f is a given continuous function, Iβ denotes the Riemann-Liouville integral of order β, and a, A, b, and B are real constants.
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