Existence results for fractional hybrid differential systems in Banach algebrasopen access
- Authors
- Bashiri, Tahereh; Vaezpour, Seiyed Mansour; Park, Choonkil
- Issue Date
- Feb-2016
- Publisher
- SPRINGEROPEN
- Keywords
- hybrid initial value problem; Banach algebras; coupled fixed point theorem; Riemann-Liouville fractional derivative
- Citation
- ADVANCES IN DIFFERENCE EQUATIONS, v.2016, no.1, pp.1 - 13
- Indexed
- SCIE
SCOPUS
- Journal Title
- ADVANCES IN DIFFERENCE EQUATIONS
- Volume
- 2016
- Number
- 1
- Start Page
- 1
- End Page
- 13
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/155205
- DOI
- 10.1186/s13662-016-0784-8
- ISSN
- 1687-1839
- Abstract
- In this manuscript we investigate the existence of solutions for the following system of fractional hybrid differential equations (FHDEs): {D-p [theta(t) w(t,theta(t))/u(t,theta(t))] = v(t, v(t)), t is an element of J, D-p [v(t)-w(t, v, (t))/u(t, v(t))] = v(t, theta(t)), t is an element of J, 0 < p < 1, theta(0) = 0, v(0) = 0, where Dr denotes the Riemann-Liouville fractional derivative of order r, J = [0, 1], and the functions u : J x R -> R \ {0}, w : J x R -> R, (0, 0) = 0 nd v : J x R -> R satisfy certain conditions. Here, we extend the Dhage hybrid fixed point theorem (Dhage in Kyungpook Math. J. 44: 145-155, 2004) and then present some results on the existence of coupled fixed points for a category of operators in Banach algebra. Also, an example is analyzed to show the use of the reported results.
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