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Lyapunov’s Inequality for a Fractional Differential Equation Subject to a Non-linear Integral Condition

Authors:
Maysaa Al Qurashi
Lakhdar Ragoub

Keywords: Lyapunov’s inequality, non linear boundary condition, Caputo fractional derivative, Green function.

Abstract:
In this paper, we investigate a Lyapunov’s inequality for a non-linear fractional differential equation, subject to the non linear integral boundary condition. Such boundary conditions are different from the ones widely considered for a class of Lyapunov’s inequality. The main tools are the Fubini’s theorem and the construction of the Green function which corresponds to the given problem in consideration. In order to illustrate this result, we give an example where we show that the non existence of non trivial solutions of an appropriate eigenvalue fractional boundary value problem obey this necessary integral condition.

Pages: 98 to 101

Copyright: Copyright (c) IARIA, 2016

Publication date: October 9, 2016

Published in: conference

ISSN: 2308-4499

ISBN: 978-1-61208-506-7

Location: Venice, Italy

Dates: from October 9, 2016 to October 13, 2016