EXISTENCE AND UNIQUENESS OF SOLUTIONS TO FRACTIONAL ORDER MULTI-POINT BOUNDARY VALUE PROBLEMS

Rahmat Ali Khan; KAMAL SHAH

Title	EXISTENCE AND UNIQUENESS OF SOLUTIONS TO FRACTIONAL ORDER MULTI-POINT BOUNDARY VALUE PROBLEMS
Publication Type	Journal Article
Year of Publication	2015
Authors	Khan, RAli, SHAH, KAMAL
Volume	19
Issue	4
Start Page	515
Pagination	11
Date Published	2015
ISSN	1083-2564
AMS	26A33, 33C45
Abstract	We study sufficient conditions for existence and uniqueness of solutions to boundary value problems for fractional order differential equations of the form$${ −^cD^q_u(t) = f(t, u(t)); \ \ \ t ∈ J = [0, 1], \ \ 1 < q ≤ 2, \\ u(0) = g(u), \ \ u(1) − \sum^{m−2}_{i=1} λ_iu(η_i) = h(u), }$$ where ${ λ_i , η_i ∈ (0, 1) }$ with ${ \sum^{m−2}_{i=1} λ_iη_i < 1, \ \ g, h ∈ C(J, \mathbb{R}) }$ are boundary functions and ${ f : J ×\mathbb{R}×\mathbb{R} → \mathbb{R} }$ is continuous. We use a fixed point theorem for condensing maps to establish sufficient conditions for existence as well as uniqueness of solutions to the boundary value problem. We provide an example to verify the applicability of our results.
URL	http://www.acadsol.eu/en/articles/19/4/4.pdf
Refereed Designation	Refereed
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