Positive solutions for mixed problems of singular fractional differential equations

Abstract

MSC (2010) 26A33, 34B16We investigate the existence of positive solutions to the singular fractional boundary value problem:x, y, z) may be singular at the value 0 of its space variables x, y, z. Here c D stands for the Caputo fractional derivative. The results are based on combining regularization and sequential techniques with a fixed point theorem on cones.

Nonlocal Fractional Boundary Value Problems with Slit-Strips Boundary Conditions

“…The literature on linear and nonlinear boundary value problems of fractional order, involving boundary conditions of diverse nature, is also quite enriched now. For some recent work on the topic, see [7,22,30,14,6,1,10,4,25,15,32] and the references therein.…”

The existence of positive solutions of singular fractional boundary value problems

“…In [31,32], the existence of positive solutions is proved by the combination of regularization and sequential techniques with the Guo-Krasnosel'skii fixed point theorem on cones.…”

“…The boundary value problems for fractional differential equations with time singularities have been discussed in [28][29][30]. However, there are a few papers [31][32][33][34][35] discussing fractional boundary value problems with nonlinearities having singularities in space variables.…”

Explicit iterations and extremal solutions for fractional differential equations with nonlinear integral boundary conditions

“…The study of boundary value problems in the setting of fractional calculus has received a great attention in the last decade and a variety of results concerning the existence of solutions, based on various analytic techniques, can be found in the literature [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The existence theory for fractional boundary value problems, no doubt, provides the basis for onward exploration of the subject.…”