Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem

Ehsan Pourhadi, Reza Saadati and Sotiris K. Ntouyas
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Ehsan Pourhadi: International Center for Mathematical Modelling in Physics and Cognitive Sciences, Department of Mathematics, Linnaeus University, SE-351 95 Växjö, Sweden
Reza Saadati: Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Mathematics, 2019, vol. 7, issue 6, 1-11

Abstract: Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative ( a C D α x ) ( t ) = f ( t , x ( t ) , x ′ ( t ) ) , a < t < b , 1 < α < 2 , x ( a ) = 0 , x ( b ) = μ x ( η ) , a < η < b , μ > λ , where λ = b − a η − a and a C D α denotes the Caputo’s fractional derivative, and f : [ a , b ] × R × R → R is a continuous function satisfying the certain conditions.

Keywords: three-point boundary-value problem; Caputo’s fractional derivative; Riemann-Liouville fractional integral; fixed-point theorems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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