IJPAM: Volume 113, No. 5 (2017)

Title

LYAPUNOV TYPE INEQUALITY
FOR HYBRID FRACTIONAL DIFFERENTIAL EQUATION
WITH PRABHAKAR DERIVATIVE

Authors

Deepak B. Pachpatte$^{1}$, Narayan G. Abuj$^{2}$, Amol D. Khandagale$^{3}$
$^{1,2,3}$Department of Mathematics
Dr. Babasaheb Ambedkar Marathwada University
Aurangabad, 431004, M.S., INDIA

Abstract

The main objective of this paper is to study the hybrid fractional boundary value problem. Lyapunov type inequality is developed involving the Prabhakar fractional derivative. Examples of our results are also given.

History

Received: October 10, 2016
Revised: January 22, 2017
Published: April 1, 2017

AMS Classification, Key Words

AMS Subject Classification: 26D10, 34B09, 33E12, 34A08
Key Words and Phrases: Lyapunov inequality, hybrid fractional differential equation, Prabhakar derivative and Mittag-Leffler function

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Bibliography

1
S. Eshaghi and A. Ansari, Lyapunov inequality for fractional differential equations with Prabhakar derivative, Math. Inequal. Appl., 1 (2016) 349-358, doi: https://doi.org/10.7153/mia-19-26.

2
R. A. C. Ferriera, A Lyapunove-type inequality for a fractional boundary value problem, Fract. Calc. Appl. Anal., 16, 4 (2013) 978-984, doi: https://doi.org/10.2478/s13540-013-0060-5.

3
R. A. C. Ferriera On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function, J. Math. Anal. Appl., 412 (2014) 1058-1063, doi: https://doi.org/10.1016/j.jmaa.2013.11.025.

4
R. Garra, R. Gorenflo, F. Polito and Z. Tomovski, Hilfer Prabhakar derivative and some applications, Appl. Math. Comput., 242 (2014) 576-589, doi: https://doi.org/10.1016/j.amc.2014.05.129.

5
M. Jleli and B. Samet, Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions, Math. Inequal. Appl., 18, 2 (2015) 443-451, doi: https://doi.org/10.7153/mia-18-33.

6
M. Jleli and B. Samet, Lyapunov-type inequalities for fractional boundary value problems, Electron. J. Differential Equations., 88 (2015) 1-11.

7
A. A. Kilbas, M. Saigo and R. K. Saxena, Generalized Mittag-Leffler function and generalized fractional calculus operators, Int. Transf. Spec. Funct. 15 (2004) 31-49, doi: https://doi.org/10.1080/10652460310001600717.

8
A.M. Lyapunov, Probleme g$\acute{e}$n$\acute{e}$ral de la stabilit$\acute{e}$ du mouvement, (French Transl. of a Russian paper dated 1893), Ann. Fac. Sci. Univ. Toulouse 2 (1907), Reprinted in: Ann. Math. studies, 17, Princeton (1947) 27-247.

9
T. R. Prabhakar, A Singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19(1971), 7-15.

10
S. Sitho, S. K Ntouyas, W. Yukunthorn and J. Tariboon, Lyapunov's type inequalities for hybrid fractional differential equation, J. Inequal. Appl., (2016) 2016:170, doi: https://doi.org/10.1186/s13660-016-1114-0.

How to Cite?

DOI: 10.12732/ijpam.v113i5.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 5
Pages: 563 - 574


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