Study of (k,Θ)-Hilfer fractional differential and inclusion systems on the glucose graph

Zhang, Lihong; Liu, Xuehui; Wang, Guotao

doi:10.1016/j.heliyon.2024.e31285

Heliyon

2024

DOI: 10.1016/j.heliyon.2024.e31285

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Study of (k,Θ)-Hilfer fractional differential and inclusion systems on the glucose graph

Lihong Zhang,

Xuehui Liu,

Guotao Wang

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2024

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Cited by 2 publications

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Existence and k‐Mittag–Leffler–Ulam stabilities of a Volterra integro‐differential equation via (k,ϱ)‐Hilfer fractional derivative

Lemnaouar

2024

Math Methods in App Sciences

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In this paper, we investigate the existence, uniqueness, and analysis of two types of ‐Mittag–Leffler–Ulam stabilities in a Volterra integro‐differential fractional differential equation that involves the ‐Hilfer operator. We utilize the Banach fixed‐point theorem to establish the existence and uniqueness of solutions. We examine the stability properties, including the ‐Mittag–Leffler–Ulam–Hyers ‐ and k‐Mittag–Leffler–Ulam–Hyers–Rassias ‐ stabilities, by employing the Grönwall–Bellman inequality. Additionally, we provide an example to confirm our findings.

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Existence and k‐Mittag–Leffler–Ulam stabilities of a Volterra integro‐differential equation via (k,ϱ)‐Hilfer fractional derivative

Lemnaouar

2024

Math Methods in App Sciences

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Some Existence Results of Coupled Hilfer Fractional Differential System and Differential Inclusion on the Circular Graph

Zhang,

Liu

2024

Qual. Theory Dyn. Syst.

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Study of (k,Θ)-Hilfer fractional differential and inclusion systems on the glucose graph

Cited by 2 publications

References 46 publications

Existence and k‐Mittag–Leffler–Ulam stabilities of a Volterra integro‐differential equation via (k,ϱ)‐Hilfer fractional derivative

Existence and k‐Mittag–Leffler–Ulam stabilities of a Volterra integro‐differential equation via (k,ϱ)‐Hilfer fractional derivative

Some Existence Results of Coupled Hilfer Fractional Differential System and Differential Inclusion on the Circular Graph

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