Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1" display="block"><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow></mml:math>-Caupto Fractional Derivative

Yang, Dandan; Bai, Chuanzhi

doi:10.1155/2019/9824623

Cited by 4 publications

(1 citation statement)

References 22 publications

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“…In the last two decades, these problems have been utilized for a wide variety of fields of science and engineering, such as underground water flow, populations dynamics and blood flow. Literature related to these problems can be found in [4,28,32,34,35].…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition

Ahmed¹,

Abdeljawad

Jarad

et al. 2020

Adv Differ Equ

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The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained.

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Section: Introductionmentioning

confidence: 99%

Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition

Ahmed¹,

Abdeljawad

Jarad

et al. 2020

Adv Differ Equ

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Controllability of coupled systems for impulsiveφ-Hilfer fractional integro-differential inclusions

Boudjerida

Seba

N’Guérékata

2020

Applicable Analysis

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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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Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative

Cited by 4 publications

References 22 publications

Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition

Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition

Controllability of coupled systems for impulsiveφ-Hilfer fractional integro-differential inclusions

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

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