Existence Results for a New Class of Boundary Value Problems of Nonlinear Fractional Differential Equations

Meysam Alvan, Rahmat Darzi and Amin Mahmoodi
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Meysam Alvan: Department of mathematics, Central Tehran Branch Islamic Azad university, Tehran 13185/768, Iran
Rahmat Darzi: Department of Mathematics, Neka Branch Islamic Azad University, Neka 48411-86114, Iran
Amin Mahmoodi: Department of mathematics, Central Tehran Branch Islamic Azad univesity, Tehran 13185/768, Iran

Mathematics, 2016, vol. 4, issue 1, 1-10

Abstract: In this article, we study the following fractional boundary value problem D 0 + α c u ( t ) + 2 r D 0 + α − 1 c u ( t ) + r 2 D 0 + α − 2 c u ( t ) = f ( t , u ( t ) ) , r > 0 , 0 t 1 , u ( 0 ) = u ( 1 ) , u ′ ( 0 ) = u ′ ( 1 ) , u ′ ( ξ ) + r u ( ξ ) = η , ξ ∈ ( 0 , 1 ) Where 2 ≤ α 3 , D 0 + α − i c ( i = 0 , 1 , 2 ) are the standard Caputo derivative and η is a positive real number. Some new existence results are obtained by means of the contraction mapping principle and Schauder fixed point theorem. Some illustrative examples are also presented.

Keywords: Fractional boundary value problem; Contraction mapping principle; Schauder fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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