Abstract
In this paper, by using the fixed-point theorem in the cone of strict-set-contraction operators, we study a class of higher-order boundary value problems of nonlinear fractional differential equation in a Banach space. The sufficient conditions for the existence of at least two positive solutions is obtained. In addition, an example to illustrate the main results is given.
Highlights
1 Introduction Fractional calculus is a generalization of ordinary differentiation and integration to arbitrary noninteger order
The fractional differential equations have been of great interest recently
There are few works that deal with the existence of solutions of nonlinear fractional differential equations in Banach spaces; see [ – ]
Summary
Fractional calculus is a generalization of ordinary differentiation and integration to arbitrary noninteger order. There are few works that deal with the existence of solutions of nonlinear fractional differential equations in Banach spaces; see [ – ]. In [ ], Hussein investigated the existence of pseudo solutions for the following nonlinear m-point boundary value problem of fractional type:. In [ ], by the monotone iterative technique and the Mönch fixed point theorem, Lv et al investigated the existence of a solution to the following Cauchy problem for the differential equation with fractional order in a real Banach space E: CDqu(t) = f t, u(t) , u( ) = u , where CDqu(t) is the Caputo derivative of order < q
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