Uniqueness of Successive Positive Solution for Nonlocal Singular Higher-Order Fractional Differential Equations Involving Arbitrary Derivatives

Abstract

In this article, by means of fixed point theorem on mixed monotone operator, we establish the uniqueness of positive solution for some nonlocal singular higher-order fractional differential equations involving arbitrary derivatives. We also give iterative schemes for approximating this unique positive solution.

Positive solutions for a boundary value problem of fractional differential equation with p-Laplacian operator

“…In consequence, fractional differential equations have been of great interest. For details, see fractional two-point boundary value problems [29,31,32,35,57,64], fractional boundary value problems at resonance [5,8,67,69,71], fractional multi-point problems with nonresonance [5,8,44,48,58,61,68], fractional initial value problems [6,7,34], fractional impulsive problems [48,72], fractional integral boundary value problems [14,40,46,62], fractional p-Laplace problems [15, 18, 20-22, 28, 36, 39, 45, 47, 49, 50, 52, 60, 65, 66, 70], fractional problems with lower and upper solution [7,39,51,59], fractional control problems, [41,43,[53][54][55][56], fractional soliton problems [19,24,26,42], fractional singular problems [17,27,30,37,…”