Nonexistence of solutions to a fractional differential boundary value problem
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Authors
Maysaa Al-Qurashi
- College of Sciences, Mathematics department, King Saud University, P. O. Box 45 180, Riyadh 11 551, Saudi Arabia.
Lakhdar Ragoub
- Mathematics Department, College of Computers and Information Systems, Al Yamamah University, P. O. Box 45 180, Riyadh 11 512, Saudi Arabia.
Abstract
We investigate new results about Lyapunov-type inequality by considering a fractional boundary value
problem subject to mixed boundary conditions. We give a necessary condition for nonexistence of solutions
for a class of boundary value problems involving Riemann-Liouville fractional order. The order considered
here is \(3 < \alpha\leq 4\). The investigation is based on a construction of Green's function and on finding its
corresponding maximum value. In order to illustrate the result, we provide an application of Lyapunov-type
inequality for an eigenvalue problem and we show how the necessary condition of existence can be employed
to determine intervals for the real zeros of the Mittag-Leffler function.
Share and Cite
ISRP Style
Maysaa Al-Qurashi, Lakhdar Ragoub, Nonexistence of solutions to a fractional differential boundary value problem, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2233--2243
AMA Style
Al-Qurashi Maysaa, Ragoub Lakhdar, Nonexistence of solutions to a fractional differential boundary value problem. J. Nonlinear Sci. Appl. (2016); 9(5):2233--2243
Chicago/Turabian Style
Al-Qurashi, Maysaa, Ragoub, Lakhdar. "Nonexistence of solutions to a fractional differential boundary value problem." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2233--2243
Keywords
- Lyapunov's inequality
- Green's function
- Riemann-Liouville derivative
- mixed boundary conditions.
MSC
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