Lyapunov-type inequalities for m-point fractional boundary value problem

Aouafi, Rabiaa; Adjeroud, Nacer

doi:10.1504/ijdsde.2019.103738

Cited by 2 publications

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“…First, based on the definitions of fractional calculus, inequality (1.2) has been extended to various forms with different fractional derivatives, such as Caputo [7,8], Hadamard [9,10], Katugampola [11], Hilfer [12,13], Caputo-Fabrizio [14], Hilfer-Katugampola [15,16], and so on. Second, under different boundary conditions, scholars studied fractional Lyapunov-type inequalities for nonlocal BVPs (multi-point BVPs [17,18] and integral BVPs [19,20]). To the best of the authors' knowledge, there are only few papers on Lyapunov-type inequalities for fractional differential equations with m-point boundary value problems in the literature; see [12,15,18].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov-type inequalities for fractional multi-point boundary value problems using a new generalized fractional derivative

2023

J. Nonlinear Funct. Anal.

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In this paper, we present a new class of fractional derivative (bi-order Hilfer-Katugampola fractional derivative). In the framework of this type of fractional calculus, we discuss a class of fractional multi-point boundary value problems (BVPs) and obtain some new fractional Lyapunov-type inequalities. Based on the generality of the definition of bi-order Hilfer-Katugampola fractional derivative, we provide a series of corollaries, which demonstrate that our results unify and generalize some known results in the existing literature.

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Section: Introductionmentioning

confidence: 99%

Lyapunov-type inequalities for fractional multi-point boundary value problems using a new generalized fractional derivative

2023

J. Nonlinear Funct. Anal.

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New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative

Zhang¹,

Zhang²,

Ni³

2021

MATH

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<abstract><p>In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.</p></abstract>

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Lyapunov-type inequalities for m-point fractional boundary value problem

Cited by 2 publications

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Lyapunov-type inequalities for fractional multi-point boundary value problems using a new generalized fractional derivative

Lyapunov-type inequalities for fractional multi-point boundary value problems using a new generalized fractional derivative

New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative

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