Existence of solutions of boundary value problems for singular fractional q-difference equations

In this paper, we study the existence and uniqueness of solutions for a class of singular three-point boundary value problems of fractional q -difference equations invovling fractional q -derivative of Riemann–Liouville type. Based on the generalization of Banach contraction principle, we obtain a s...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2017-06, Vol.54 (1-2), p.23-40
Main Authors: Ma, Kuikui, Sun, Shurong, Han, Zhenlai
Format: Article
Language:English
Subjects:
Applied mathematics
Banach spaces
Boundary value problems
Computational Mathematics and Numerical Analysis
Difference equations
Existence theorems
Fixed points (mathematics)
Mathematical analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Theory of Computation
Uniqueness
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Summary:In this paper, we study the existence and uniqueness of solutions for a class of singular three-point boundary value problems of fractional q -difference equations invovling fractional q -derivative of Riemann–Liouville type. Based on the generalization of Banach contraction principle, we obtain a sufficient condition for existence and uniqueness of solutions of the problem. By applying the Krasnoselskii’s fixed point theorem, we establish a sufficient condition for the existence of at least one solution of the problem. As applications, two examples are presented to illustrate our main results.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-016-0994-y