Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation

By Xiaojie Xu, Daqing Jiang, Chengjun Yuan. 2009

237 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/eca7ff97d522446a9ee260b3305e1f285a255ea2

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

SOLUTIONS TO A DISCRETE RIGHT-FOCAL FRACTIONAL BOUNDARY VALUE PROBLEM (2010, unknown): “However, only in recent years has there been an explosion of research in this area – see, for example, [2, 8, 9, 17, 21] and the references therein.”
Fractional boundary value problems with singularities in space variables (2012, unknown): “Paper [30] deals with the problem Du = f (t, u), u(0) = u′(0) = 0, u(1) = u′(1) = 0, where 3 < α ≤ 4 and f ∈ C([0,1] × (0,∞)).”
On a discrete fractional three-point boundary value problem (2012, background): “For example, the papers [2,11,12,14,17,24,30] each attend to various theoretical properties of the continuous fractional calculus.”
Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p-Laplacian operator (2017, background): “4 ([17, 33]) The function G1(t, s) defined by (2.”
Positive solutions for mixed problems of singular fractional differential equations (2012, background): “However only a few papers [1], [12], [13] consider boundary value problems for fractional differential equations with the nonlinearities having singularities in space variables.”
Positive solutions of m-point boundary value problems for a class of nonlinear fractional differential equations (2004, background): “1 in [4], we can show that A : P → P .”
The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems (2016, background): “Because of the crucial role played by nonlinear equations in applied science as well as mathematics, nonlinear functional analysis has been an active area of research, and nonlinear operators with connection to nonlinear (fractional) differential and integral equations have been extensively studied ”