A new conversation on the existence of Hilfer fractional stochastic Volterra–Fredholm integro-differential inclusions via almost sectorial operators

Sivasankar, Sivajiganesan; Udhayakumar, R.; Muthukumaran, V.

doi:10.15388/namc.2023.28.31450

Cited by 4 publications

(3 citation statements)

References 27 publications

(42 reference statements)

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“…There have been several investigations conducted to find out if there are solutions for fractional differential systems as well as fractional differential inclusions. The following research publications can be referenced to support the concept and the implications discussed in relation to fractional calculus: [7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

Varun Bose,

Udhayakumar,

Muthukumaran

et al. 2024

Contemp. Math.

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In this article, we studied the approximate controllability of Ψ-Caputo fractional differential systems. We prove the sufficient conditions for an abstract Cauchy problem invloving infinite delay, impulsive and nonlocal conditions. The result is shown by means of the infinitesimal operator, semigroup theory, fractional calculus, and Schauder’s fixed point theorem. First, we prove the existence of the mild solution and demonstrate that the Ψ-Caputo fractional system is approximately controllable. Finally, an example is given to analyse the obtained results.

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Section: Introductionmentioning

confidence: 99%

A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

Varun Bose,

Udhayakumar,

Muthukumaran

et al. 2024

Contemp. Math.

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“…For other publications on antiperiodic solutions and differential inclusions involving Hilfer fractional derivatives, we refer to [35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Antiperiodic Solutions for Impulsive ω-Weighted ϱ–Hilfer Fractional Differential Inclusions in Banach Spaces

Alsheekhhussain,

Ibrahim,

Al-Sawalha

et al. 2024

Fractal Fract

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In this article, we construct sufficient conditions that secure the non-emptiness and compactness of the set of antiperiodic solutions of an impulsive fractional differential inclusion involving an ω-weighted ϱ–Hilfer fractional derivative, D0,tσ,v,ϱ,ω, of order σ∈(1,2), in infinite-dimensional Banach spaces. First, we deduce the formula of antiperiodic solutions for the observed problem. Then, we give two theorems regarding the existence of these solutions. In the first, by using a fixed-point theorem for condensing multivalued functions, we show the non-emptiness and compactness of the set of antiperiodic solutions; and in the second, by applying a fixed-point theorem for contraction multivalued functions, we prove the non-emptiness of this set. Because many types of famous fractional differential operators are particular cases from the operator D0,tσ,v,ϱ,ω, our results generalize several recent results. Moreover, there are no previous studies on antiperiodic solutions for this type of fractional differential inclusion, so this work is novel and interesting. We provide two examples to illustrate and support our conclusions.

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“…Ironically, the integral form appears in the majority of the formulations of fractional derivatives. Readers are directed to [3][4][5] for a comprehensive understanding of fractional calculus and [6][7][8][9][10][11][12][13][14][15][16] for an overview of fractional differential equations (FDEs).…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Neutral Differential Systems with Fractional Deformable Derivatives

Raju,

Sevugan,

Udhayakumar

et al. 2023

Fractal Fract

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This article deals with the existence and uniqueness of solutions, as well as the approximate controllability of fractional neutral differential equations (ACFNDEs) with deformable derivatives. The findings are achieved using Banach’s, Krasnoselskii’s, and Schauder’s fixed-point theorems and semigroup theory. Three numerical examples are used to illustrate the application of the theories discussed in the conclusion.

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A new conversation on the existence of Hilfer fractional stochastic Volterra–Fredholm integro-differential inclusions via almost sectorial operators

Cited by 4 publications

References 27 publications

A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

Antiperiodic Solutions for Impulsive ω-Weighted ϱ–Hilfer Fractional Differential Inclusions in Banach Spaces

Approximate Controllability of Neutral Differential Systems with Fractional Deformable Derivatives

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