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14 Aug 2012
Existence of solutions of twopoint boundary value problems for fractional pLaplace differential equations at resonance
 Xiaosong Tang,
 Changyuan Yan,
 Qing Liu
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In this paper, we consider the following twopoint boundary value problem for fractional pLaplace differential equation where \(D^{\alpha}_{0^{+}}\) , \(D^{\beta}_{0^{+}}\) denote the Caputo fractional derivatives, 0<α,β≤1, 1<α+β≤2. By using the coincidence degree theory, a new result on the existence of solutions for above fractional boundary value problem is obtained. These results extend the corresponding ones of ordinary differential equations of integer order. Finally, an example is inserted to illustrate the validity and practicability of our main results.
Supported by the Youth NSF of Jiangxi Province (20114BAB211015), the Youth NSF of the Education Department of Jiangxi Province (GJJ11180), the NSF of Jinggangshan University.
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 Preliminary results
 Some lemmas
 Main result and example
 References
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 Title
 Existence of solutions of twopoint boundary value problems for fractional pLaplace differential equations at resonance
 Journal

Journal of Applied Mathematics and Computing
Volume 41, Issue 12 , pp 119131
 Cover Date
 20130301
 DOI
 10.1007/s1219001205980
 Print ISSN
 15985865
 Online ISSN
 18652085
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Caputo fractional derivative
 pLaplace differential equation
 Twopoint boundary value problem
 Resonance
 Coincidence degree theory
 34A08
 34B15
 Authors

 Xiaosong Tang ^{(1)}
 Changyuan Yan ^{(1)}
 Qing Liu ^{(2)}
 Author Affiliations

 1. College of Mathematics and Physics, Jinggangshan University, Ji’an, Jiangxi, 343009, P.R. China
 2. College of Electronics and Information Engineering, Jinggangshan University, Ji’an, Jiangxi, 343009, P.R. China