Abstract
In this paper, we establish sufficient conditions for the existence and uniqueness of solution of a boundary value problem of differential equations of fractional order involving the nonlocal boundary condition.
Highlights
Sachin Kumar Verma, Ramesh Kumar Vats and Ankit Kumar Nain abstract: In this paper, we consider a boundary value problem of differential equations of fractional order involving the nonlocal boundary condition
In boundary value problem (1.2), the authors consider fractional order derivative but in BVP (1.1) cabrera et al consider the ordinary derivative of fourth order
Definition 2.1. ( [21]) For a continuous function f : [0, ∞) → R, the Caputo derivative of fractional order q is defined as cDqf (t) = 1 t (t − s)n−q−1f (n)(s)ds, n = [q] + 1
Summary
Sachin Kumar Verma, Ramesh Kumar Vats and Ankit Kumar Nain abstract: In this paper, we consider a boundary value problem of differential equations of fractional order involving the nonlocal boundary condition. We establish sufficient conditions for the existence of solution of the boundary value problem with the help of Schaefer’s fixed point theorem. Our uniqueness result is based on contraction mapping principle. In boundary value problem (1.2), the authors consider fractional order derivative but in BVP (1.1) cabrera et al consider the ordinary derivative of fourth order.
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