Monotone Iterative and Upper–Lower Solution Techniques for Solving the Nonlinear ψ-Caputo Fractional Boundary Value Problem
Keyword(s):
The objective of this paper is to study the existence of extremal solutions for nonlinear boundary value problems of fractional differential equations involving the ψ−Caputo derivative CDa+σ;ψϱ(t)=V(t,ϱ(t)) under integral boundary conditions ϱ(a)=λIν;ψϱ(η)+δ. Our main results are obtained by applying the monotone iterative technique combined with the method of upper and lower solutions. Further, we consider three cases for ψ*(t) as t, Caputo, 2t, t, and Katugampola (for ρ=0.5) derivatives and examine the validity of the acquired outcomes with the help of two different particular examples.
2016 ◽
Vol 56
(2)
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pp. 143-163
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2013 ◽
Vol 222
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pp. 72-81
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