Anti-periodic boundary value problems for Caputo-Fabrizio fractional impulsive differential equations

Benyoub, Mohammed; Belghaba, Kacem

doi:10.5937/matmor2202049b

Cited by 1 publication

(2 citation statements)

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“…II. Extend the recent work performed in [26,28,32,33] when the considered fractional differential operator is replaced by D θ,v,ϱ,ω ξ i ,ξ and the space dimension is made infinite. III.…”

Section: Discussionmentioning

confidence: 92%

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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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Section: Discussionmentioning

confidence: 92%

“…Here, we mention some other studies on antiperiodic solutions of fractional differential equations and differential inclusions. Benyoub et al [32] discussed the existence and uniqueness of solutions for a nonlinear antiperiodic boundary-value problem for fractional impulsive differential equations:…”

Section: Introductionmentioning

confidence: 99%