Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 16 (2021), 43 -- 93

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This work is licensed under a Creative Commons Attribution 4.0 International License.

LYAPUNOV-TYPE INEQUALITIES FOR FRACTIONAL DIFFERENTIAL EQUATIONS: A SURVEY

Sotiris K. Ntouyas and Bashir Ahmad

Abstract. A survey of results on Lyapunov-type inequalities for fractional differential equations associated with a variety of boundary conditions is presented. We have included some recent work on the topic dealing with sequential, Caputo-Fabrizio, Hadamard, Hilfer, Katugampola, hyprid, or nested fractional derivatives. We have also focused on Lyapunov-type inequalities for problems containing fractional derivatives with respect to a certain function, systems of fractional differential equations, and conformable derivatives. Furthermore, Lyapunov-type inequalities for fractional differential equations based on non Green function approach are discussed.

2020 Mathematics Subject Classification: 26A33; 34A08; 26D10; 33E12; 34B27
Keywords: Lyapunov-type inequality; fractional derivative; fractional integral; Green’s function; fractional boundary value problem; eigenvalue problem

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Sotiris K. Ntouyas
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece.
e-mail: sntouyas@uoi.gr
and
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group,
Department of Mathematics, Faculty of Science, King Abdulaziz University,
P.O. Box 80203, Jeddah 21589, Saudi Arabia.

Bashir Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group,
Department of Mathematics, Faculty of Science, King Abdulaziz University,
P.O. Box 80203, Jeddah 21589, Saudi Arabia.
e-mail: bashirahmad_qau@yahoo.com


http://www.utgjiu.ro/math/sma