Existence and stability of a q-Caputo fractional jerk differential equation having anti-periodic boundary conditions

Khalid, Khansa Hina; Zada, Akbar; Popa, Ioan-Lucian; Samei, Mohammad Esmael

doi:10.1186/s13661-024-01834-6

Cited by 6 publications

(1 citation statement)

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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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“…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%