On the nonlinear sequential ψ-Hilfer fractional differential equations

Abbas, Mohamed I.

doi:10.12988/ijma.2020.91283

Cited by 11 publications

(2 citation statements)

References 2 publications

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“…In [28], the authors discussed the existence, uniqueness and UHR stability results for ψ-Hilfer problem via a generalized Gronwall inequality. Moreover, they discussed some important qualitative properties of solutions such as existence, uniqueness, and stability results in the following chain [15,18,19,25,28,29,30,31,32,33,34]. Recently Gao et al, in [35] established the existence and uniqueness of solutions to the Hilfer nonlocal boundary value problem…”

Section: Introductionmentioning

confidence: 99%

Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions

Almalahi

Panchal

2020

J. Math. Anal. Model.

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In this paper, we study the class of boundary value problems for a nonlinear implicit fractional differential equation with periodic conditions involving a ψ-Hilfer fractional derivative. With the help of properties Mittag-Leffler functions, and fixed-point techniques, we establish the existence and uniqueness results, whereas the generalized Gronwall inequality is applied to get the stability results. Also, an example is provided to illustrate the obtained results.

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Section: Introductionmentioning

confidence: 99%

Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions

Almalahi

Panchal

2020

J. Math. Anal. Model.

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“…For instance, we mention here few recent works by Abbas, M.I. [1] - [7], also see the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Four-point boundary value problems for a coupled system of fractional differential equations with $ψ$-Caputo fractional derivatives

Abbas¹

2020

Preprint

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In this paper, we focus on the existence and uniqueness of solutions of boundary value problems for a coupled system of fractional differential equations with four-point boundary conditions involving ψ-Caputo fractional derivatives. Our investigation is based on Leray-Schauder alternative and Banach's fixed point theorem. Two examples are presented to illustrate the applicability of the results developed.

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Existence results for nonlinear neutral generalized Caputo fractional differential equations

Adjimi

Boutiara

Abdo

et al. 2021

J. Pseudo-Differ. Oper. Appl.

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On the nonlinear sequential ψ-Hilfer fractional differential equations

Cited by 11 publications

References 2 publications

Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions

Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions

Four-point boundary value problems for a coupled system of fractional differential equations with $ψ$-Caputo fractional derivatives

Existence results for nonlinear neutral generalized Caputo fractional differential equations

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