Abstract
In this paper we investigate a new kind of nonlocal multi-point boundary value problem of Caputo type sequential fractional integro-differential equations involving Riemann-Liouville integral boundary conditions. Several existence and uniqueness results are obtained via suitable fixed point theorems. Some illustrative examples are also presented. The paper concludes with some interesting observations.
Highlights
Fractional differential equations arise in many engineering and scientific disciplines such as physics, chemistry, aerodynamics, electrodynamics of complex medium or polymer rheology
Sequential fractional differential equations are found to be of much interest [, ]
We investigate the existence and uniqueness of solutions for a sequential fractional differential equation of the form cDq + kcDq– x(t) = f t, x(t), cDβ x(t), Iγ x(t), t ∈ [, ], < q ≤, < β, γ , ( . )
Summary
Fractional differential equations arise in many engineering and scientific disciplines such as physics, chemistry, aerodynamics, electrodynamics of complex medium or polymer rheology. In [ ], the authors studied different kinds of boundary value problems involving sequential fractional differential equations. In a recent article [ ], the existence of solutions for higher-order sequential fractional differential inclusions with nonlocal three-point boundary conditions was discussed. Ahmad et al Boundary Value Problems (2016) 2016:205 subject to nonlocal multi-point and Riemann-Liouville type integral boundary conditions: x( ) = , x ( ) = , m η (η – s)δ–. 2 Background material This section is devoted to some fundamental concepts of fractional calculus [ ] and a basic lemma related to the linear variant of the given problem. For any y ∈ C([ , ], R), a function x ∈ C ([ , ], R) is a solution of linear sequential fractional differential equation cDq + kcDq– x(t) = y(t), subject to the boundary conditions
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