Existence and multiplicity of solutions for fractional differential equations with parameters

Yan, Rian; Sun, Shurong; Sun, Ying

doi:10.1007/s12190-015-0894-6

Cited by 4 publications

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many interesting results of the existence of positive solutions of various classes of fractional differential equations with or without the integral boundary condition have been discussed. Among these works (see [6][7][8][9][10][11][12][13][14][15][16][17]) and the references therein. For example in [12], Nan and Wang studied the existence and uniqueness of a positive solution for the following nonlinear fractional differential equations where 0 < α < 1, D α 0 + is the standard Riemann-Liouville fractional derivative and f : [0, 1] × R + −→ R + is continuous.…”

Section: Introductionmentioning

confidence: 99%

Positive solution of a fractional differential equation with integral boundary conditions

Abdo¹,

Wahash²,

Panchal³

2018

J. Appl. Math. Comput. Mech.

View full text Add to dashboard Cite

In this paper, we prove the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional differential equations involving a Caputo fractional operator with integral boundary conditions. The technique used to prove our results depends on the upper and lower solution, the Schauder fixed point theorem and the Banach contraction principle. The result of existence obtained through constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Illustrative examples are provided. MSC 2010: 34A08, 34B15, 34B18, 47H10 Keywords: fractional derivative and integral, positive solutions of nonlinear boundary value problems, upper and lower solutions, fixed point theorem

show abstract