Existence for fractional Dirichlet boundary value problem under barrier strip conditions

Abstract

In this paper, a fixed-point theorem is used to establish existence results for fractional Dirichlet boundary value problemwhere 1 < α 2, D α x(t) is the conformable fractional derivative, and f : [0, 1] × R 2 → R is a continuous function. The main condition is sign condition. The method used is based upon the theory of fixed-point index.

A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function

“…Later on, the above results were extended to a fractional case in [17,32,33], to a one-sided case in [7], and to a high dimensional case in [34]. For other interesting works we can consult [19,20,[35][36][37]. In particular, Liu and Mao [7] investigated the regularity of the one-dimensional discrete one-sided Hardy-Littlewood maximal operator…”

Positive solutions of fractional differential equations involving the Riemann–Stieltjes integral boundary condition

“…In [2], by means of a fixed point theorem, Bai is the Riemann-Liouville fractional derivative, f is a Carathédory function, and f (t, x, y, z) is singular at the value 0 of its arguments x, y, z. Some recent contributions of fractional differential equations can be seen in [1][2][3][4][5][6][7][8][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Multiplicity for fractional differential equations with p-Laplacian

“…Many papers and books on fractional calculus and fractional differential equations have appeared recently. For an introduction of fractional calculus and fractional differential equations, we refer the reader to [17,25] and the references therein. And there have been many results on existence and uniqueness of the solution of boundary value problems for fractional differential equations.…”