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A coupled fixed point theorem and application to fractional hybrid differential problems
- Authors
- Bashiri, T.; Vaezpour, S.M.; Park, C.
- Issue Date
- Mar-2016
- Publisher
- Hindawi Publishing Corporation
- Keywords
- hybrid initial value problem; Banach space; coupled fixed point theorem; Riemann-Liouville fractional derivative
- Citation
- Fixed Point Theory and Applications, v.2016, no.1, pp 1 - 11
- Pages
- 11
- Indexed
- SCIE
SCOPUS
- Journal Title
- Fixed Point Theory and Applications
- Volume
- 2016
- Number
- 1
- Start Page
- 1
- End Page
- 11
- ISSN
- 1687-1820
1687-1812
- Abstract
- This paper is devoted to the study of the existence of solution to the following system of fractional hybrid differential equations: (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) where (Formula presented.) is the R-L fractional derivative of order α, (Formula presented.) , (Formula presented.) , and the functions (Formula presented.) , (Formula presented.) and (Formula presented.) satisfy certain conditions. The proof of the existence theorem is based on a coupled fixed point theorem of Krasnoselskii type, which extends a fixed point theorem of Burton (Appl. Math. Lett. 11:85-88, 1998). Finally, our results are illustrated by a concrete example.
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