On the Existence of Solutions for Impulsive Fractional Differential Equations

Abstract

We are concerned with a type of impulsive fractional differential equations attached with integral boundary conditions and get the existence of at least one positive solution via global bifurcation techniques.

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

“…For the convenience of the reader, we only present here some necessary properties from fractional calculus theory in the sense of Riemann-Liouville, and the corresponding definitions can be found in [76] or [12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

“…In the aspect of mathematical theory and application, to obtain further information of the relative natural phenomena, many authors are interested in the existence and properties of solutions for fractional differential models [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and many analytical techniques and methods have been developed to solve various differential equations, such as iterative methods [28][29][30][31][32][33][34][35][36][37], the Mawhin continuation theorem for resonance [38][39][40], the topological degree method [41,42], the fixed point theorem [43][44][45][46][47][48][49][50][51][52][53][54][55], the variational method [56][57][58]…”

The Unique Positive Solution for Singular Hadamard Fractional Boundary Value Problems

“…In the past ten years, fractional differential equations have been considered in many papers (see [11][12][13][14][15][16][17][18][19][20][21][22]). Most of the works on the topic have been based on Riemann-Liouville type and Caputo type fractional differential equations.…”

Solutions for a class of fractional Langevin equations with integral and anti-periodic boundary conditions

“…There are a lot of good research results on boundary value problems of fractional differential equations . Recently fractional Langevin equations have been studied by some scholars (see, for example, [25][26][27]).…”