A remark on <i><b>ψ</b></i>–Hilfer fractional differential equations with non‐instantaneous impulses

Hoa, Ngo Van; O’Regan, Donal

doi:10.1002/mma.6125

Cited by 14 publications

(4 citation statements)

References 19 publications

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“…Differential equations concerning the ψ-Hilfer fractional derivative D σ,v,ψ 0,ϱ , σ ∈ (0, 1), υ ∈ [0, 1], without impulses are studied in [37][38][39][40], with instantaneous impulses in [41] and with non-instantaneous impulses in [41][42][43][44][45]. Also, Sitho [46] studied implicit fractional integro-differential equations with the ψ-Hilfer fractional derivative D σ,v,ψ 0,ϱ without impulses and σ ∈ (1, 2),υ ∈ [0, 1].…”

Section: Introductionmentioning

confidence: 99%

The Existence of Solutions for w-Weighted ψ-Hilfer Fractional Differential Inclusions of Order μ ∈ (1, 2) with Non-Instantaneous Impulses in Banach Spaces

Alsheekhhussain,

Ibrahim,

Al-Sawalha

et al. 2024

Fractal Fract

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In this research, we obtain the sufficient conditions that guarantee that the set of solutions for an impulsive fractional differential inclusion involving a w-weighted ψ-Hilfer fractional derivative, D0,tσ,v,ψ,w,of order μ∈(1,2), in infinite dimensional Banach spaces that are not empty and compact. We demonstrate the exact relation between a differential equation involving D0,tσ,v,ψ,w of order μ ∈(1,2) in the presence of non-instantaneous impulses and its corresponding fractional integral equation. Then, we derive the formula for the solution for the considered problem. The desired results are achieved using the properties of the w-weighted ψ-Hilfer fractional derivative and appropriate fixed-point theorems for multivalued functions. Since the operator D0,tσ,v,ψ,w includes many types of well-known fractional differential operators, our results generalize several results recently published in the literature. We give an example that illustrates and supports our theoretical results.

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Section: Introductionmentioning

confidence: 99%

The Existence of Solutions for w-Weighted ψ-Hilfer Fractional Differential Inclusions of Order μ ∈ (1, 2) with Non-Instantaneous Impulses in Banach Spaces

Alsheekhhussain,

Ibrahim,

Al-Sawalha

et al. 2024

Fractal Fract

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“…For more recent contributions relevant to non-instantaneous impulsive fractional differential equations, we refer the reader to the papers [11,13,16,20,21] and references cited therein. Motivated by the above papers, we investigate the following non-instantaneous impulsive fractional integro-differential equation:…”

Section: Introductionmentioning

confidence: 99%

Non-instantaneous impulsive fractional integro-differential equations with proportional fractional derivatives with respect to another function

Abbas

2023

Stud. Univ. Babes-Bolyai Math.

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"This paper concerns the existence and uniqueness of solutions of non- instantaneous impulsive fractional integro-di erential equations with proportional fractional derivatives with respect to another function. By the aid of the nonlinear alternative of Leray-Schauder type and the Banach contraction mapping principle, the main results are demonstrated. Two examples are inserted to illustrate the applicability of the theoretical results."

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“…For more recent contributions relevant to non‐instantaneous impulsive fractional differential equations, we refer the reader to previous papers 16–20 and references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Non‐instantaneous impulsive fractional integro‐differential equations with proportional fractional derivatives with respect to another function

Abbas

2021

Math Methods in App Sciences

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This paper concerns the existence and uniqueness of solutions of non‐instantaneous impulsive fractional integro‐differential equations with proportional fractional derivatives with respect to another function. By the aid of the nonlinear alternative of Leray‐Schauder type and the Banach contraction mapping principle, the main results are demonstrated. Two examples are inserted to illustrate the applicability of the theoretical results.

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A remark on ψ–Hilfer fractional differential equations with non‐instantaneous impulses

Abstract: We present a reasonable concept for solutions of non‐instantaneous impulsive Cauchy problems with a ψ–Hilfer fractional derivative. Also, we provide a new sufficient condition for the existence, uniqueness, and stability of solutions for the given problem.

Cited by 14 publications

References 19 publications

The Existence of Solutions for w-Weighted ψ-Hilfer Fractional Differential Inclusions of Order μ ∈ (1, 2) with Non-Instantaneous Impulses in Banach Spaces

The Existence of Solutions for w-Weighted ψ-Hilfer Fractional Differential Inclusions of Order μ ∈ (1, 2) with Non-Instantaneous Impulses in Banach Spaces

Non-instantaneous impulsive fractional integro-differential equations with proportional fractional derivatives with respect to another function

Non‐instantaneous impulsive fractional integro‐differential equations with proportional fractional derivatives with respect to another function

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