Nontrivial solutions for an integral boundary value problem involving Riemann–Liouville fractional derivatives

Abstract

In this paper using topological degree we study the existence of nontrivial solutions for a fractional differential equation involving integral boundary conditions. Here, the nonlinear term may be sign-changing and may also depend on the derivatives of the unknown function.

Variational Methods for an Impulsive Fractional Differential Equations with Derivative Term

“…In particular, the solvability, attractivity, and multiplicity of solutions for FDEs have been greatly discussed. We refer to the monographs of Podlubny [1], Kilbas et al [2], Diethelm [3], Zhou [4], the papers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein.…”

Explicit monotone iterative sequences for positive solutions of a fractional differential system with coupled integral boundary conditions on a half-line

“…On the other hand, integral boundary conditions are considered to be more reasonable than the local boundary conditions, which can depict phenomena of heat transmission, population dynamics, blood flow, etc. A large number of results about fractional differential equations with integral boundary condition have been obtained, see [9,10,[30][31][32][33][34][35][36][37][38][39][40][41][42][43] and the references cited therein. Meanwhile, we note that the coupled systems of fractionalorder differential equations have also attracted much attention due to their extensive applications, we refer to [3,9,10,14,22,29,[32][33][34][35][36][37][38][39][40][41][42][43].…”

Positive solutions for a class of fractional difference systems with coupled boundary conditions

“…. , b} with ba ∈ N 1 . In this paper we study the existence of positive solutions for the following fractional difference system with coupled boundary conditions: -3 x(t) = f 1 (t + ν -1, x(t + ν -1), y(t + ν -1)), t ∈ [0, T -1] N 0 , -ν ν-3 y(t) = f 2 (t + ν -1, x(t + ν -1), y(t + ν -1)), t ∈ [0, T -1] N 0 , x(ν -3) = [ α ν-3 x(t)]| t=ν-α-2 = 0, y(ν -3) = [ α ν-3 y(t)]| t=ν-α-2 = 0, x(T + ν -1) = ay(ξ + ν), y(T + ν -1) = bx(η + ν),…”

“…In recent years, the fractional calculus and fractional differential equations have been of great interest in the literature, and they have been widely applied in numerous diverse fields including electrical engineering, chemistry, mathematical biology, control theory, and the calculus of variations. For example, papers [1,2] have introduced a fractional order model for infection of CD4 + T cells in HIV, which can be depicted by the system where D α i are fractional derivatives, i = 1, 2, 3. Till now, we have noted that by using the techniques of nonlinear analysis, a large number of results concerning the existence and multiplicity of solutions (or positive solutions) of nonlinear fractional differential equations can be found in the literature, we refer the reader to and the references cited therein.…”