A singular boundary value problem for nonlinear differential equations of fractional order

Abstract

We are concerned with the nonlinear differential equation of fractional orderis the Riemann-Liouville fractional order derivative, subject to the boundary conditionsWe obtain the existence of at least one solution using the Leray-Schauder Continuation Principle.

Positive solutions for mixed problems of singular fractional differential equations

“…We note that in contrast to papers dealing with fractional differential equations for 1 < α < 2 (with the exception of [8]), the nonlinearity f in (1.1) depends on the derivative of u. Due to this fact we need to assume that f is a L q -Carathéodory function with q > 1 α −1 .…”

Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

“…Recently, the theory of fractional differential equations has been developed very quickly and the investigation for the existence of solutions of these differential equations has attracted considerable attention of researchers in the last few years (see [1][2][3][4][5][6][7][8][9][10][11] and the references therein).…”

A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations

“…Fractional differential equations arise in many fields, such as physics, mechanics, chemistry, economics, engineering, and biological sciences; see [1][2][3][4][5][6], for example. In the recent years, there has been a significant development in ordinary and partial differential equations involving fractional derivatives; see the monographs of Miller and Ross [3], Podlubny [5], Kilbas et al [6], and the papers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the references therein. In these papers, many authors have investigated the existence of positive solutions for nonlinear fractional differential equation boundary value problems.…”