Existence criteria of solutions for a fractional nonlocal boundary value problem and degeneration to corresponding integer-order case

Abstract

In this paper, we mainly discuss the existence and uniqueness results of solutions to fractional differential equations with multi-strip boundary conditions. When the fractional order α becomes integer, the existence theorem of positive solutions can be established by a monotone iterative technique. Also, some examples are presented to illustrate the main results.

Positive solutions to n-dimensional $\alpha _{1}+\alpha _{2}$ order fractional differential system with p-Laplace operator

“…Fractional differential models can always make the description more accurate, and make the physical significance of parameters more explicit than the integer order ones. So, many monographs and literature works have appeared on fractional calculus and fractional differential equations, see [1][2][3][4][5][6].…”

Positive Solutions to a Coupled Fractional Differential System with p-Laplacian Operator

“…By reading the existing literatures [11][12][13][14][15][16][17][18][19][20][21][22][23][24], we note that the fractional differential system involving -Laplacian operator and multistrip and multipoint boundary conditions has not been studied yet. Thus, in this paper, we first pay close attention to the following fractional differential system, involving -Laplacian operator and lower fractional derivatives:…”