Abstract
This paper investigates the solvability of a class of higher-order fractional two-point boundary value problem (BVP), and presents several new results. First, Green’s function of the considered BVP is obtained by using the property of Caputo derivative. Second, based on Schaefer’s fixed point theorem, the solvability of the considered BVP is studied, and a sufficient condition is presented for the existence of at least one solution. Finally, an illustrative example is given to support the obtained new results.
Highlights
Fractional differential equations (FDEs) have been of great interest recently
This paper investigates the solvability of a class of higher-order fractional two-point boundary value problem (BVP), and presents several new results
The first issue for the theory of fractional differential equations is the existence of solutions to kinds of boundary value problems (BVPs), which has been studied recently by many scholars [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18], and lots of excellent results have been obtained by means of fixed-point theorems, Leray-Schauder theory, upper and lower solutions technique, and so forth
Summary
Fractional differential equations (FDEs) have been of great interest recently. This is due to the development of the theory of fractional calculus itself as well as its applications [1,2,3]. This paper investigates the solvability of a class of higher-order fractional two-point boundary value problem (BVP), and presents several new results. Green’s function of the considered BVP is obtained by using the property of Caputo derivative. Based on Schaefer’s fixed point theorem, the solvability of the considered BVP is studied, and a sufficient condition is presented for the existence of at least one solution.
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