On Nonlinear Ψ-Caputo Fractional Integro Differential Equations Involving Non-Instantaneous Conditions

Arul, Ramasamy; Karthikeyan, P.; Karthikeyan, Kulandhaivel; Geetha, Palanisamy; Alruwaily, Ymnah; Almaghamsi, Lamya; El‐hady, El‐sayed

doi:10.3390/sym15010005

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…In [26], FPTs played a basic role in proving the stability of many fractional-order systems, and in proving the existence and uniqueness results for some of these systems. In [27], the authors employed FPTs to study the existence and uniqueness of the solution of some fractional integral DEs involving non-instantaneous impulsive boundary conditions (N-IIBC). Known FPTs have been used in [28] to study some fractional DEs with fractional boundary conditions (FBCs).…”

Section: Introductionmentioning

confidence: 99%

Stability in the Sense of Hyers–Ulam–Rassias for the Impulsive Volterra Equation

El-hady,

Öğrekçi,

Lazăr

et al. 2024

Fractal Fract

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Section: Introductionmentioning

confidence: 99%

Stability in the Sense of Hyers–Ulam–Rassias for the Impulsive Volterra Equation

El-hady,

Öğrekçi,

Lazăr

et al. 2024

Fractal Fract

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“…The E-UR of the solution of some fractional integro differential equations involving non-instantaneous impulsive boundary conditions have been studied in [27] by some FPTs. See also [28], where the sequential Caputo-Hadamard FDE with fractional boundary conditions have been examined using FPTs.…”

Section: Introductionmentioning

confidence: 99%

Some Results on Fractional Boundary Value Problem for Caputo-Hadamard Fractional Impulsive Integro Differential Equations

Alruwaily,

Venkatachalam,

El-hady

2023

Fractal Fract

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The results for a new modeling integral boundary value problem (IBVP) using Caputo-Hadamard impulsive fractional integro-differential equations (C-HIFI-DE) with Banach space are investigated, along with the existence and uniqueness of solutions. The Krasnoselskii fixed-point theorem (KFPT) and the Banach contraction principle (BCP) serve as the basis of this unique strategy, and are used to achieve the desired results. We develop the illustrated examples at the end of the paper to support the validity of the theoretical statements.

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Existence and uniqueness for a coupled system of fractional equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions

Alruwaily

Almaghamsi

Karthikeyan

et al. 2023

MATH

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<abstract><p>Recently, coupled systems of fractional differential equations play a central role in the modelling of many systems in e.g., financial economics, ecology, and many more. This study investigates the existence and uniqueness of solutions for a nonlinear coupled system of fractional differential equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions. The main tools are known fixed point theorems, namely, Leray-Schauder alternative, Banach fixed point theorem, and the Krasnoselskii fixed point theorem. The new system, which can be considered as a generalized version of many previous fascinating systems, is where the article's novelty lies. Examples are presented to illustrate the results. In this way, we generalize several earlier results.</p></abstract>

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On Nonlinear Ψ-Caputo Fractional Integro Differential Equations Involving Non-Instantaneous Conditions

Cited by 3 publications

References 33 publications

Stability in the Sense of Hyers–Ulam–Rassias for the Impulsive Volterra Equation

Stability in the Sense of Hyers–Ulam–Rassias for the Impulsive Volterra Equation

Some Results on Fractional Boundary Value Problem for Caputo-Hadamard Fractional Impulsive Integro Differential Equations

Existence and uniqueness for a coupled system of fractional equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions

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