On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations

Kishor D. Kucche, Ashwini D. Mali, Arran Fernandez and Hafiz Muhammad Fahad

Chaos, Solitons & Fractals, 2022, vol. 163, issue C

Abstract: We investigate the Hilfer-type operator within the topic of tempered fractional calculus with respect to functions. This operator, the tempered Ψ-Hilfer derivative, is defined for the first time here, and its fundamental properties are studied, such as composition properties, function space mappings, and other functional analysis properties. We also consider fractional differential equations involving these operators, and establish existence, uniqueness, well-posedness, and stability results for such equations under suitable conditions.

Keywords: Fractional differential equations; Tempered fractional calculus; Hilfer fractional derivative; Fractional calculus with respect to a function; Existence and uniqueness; Well-posedness; Ulam stability (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:163:y:2022:i:c:s096007792200741x

DOI: 10.1016/j.chaos.2022.112547

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