On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations. (October 2022) - Kucche, Kishor D.; Mali, Ashwini D.; Fernandez, Arran; Fahad, Hafiz Muhammad
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. Highlights: We introduced the tempered Ψ -Hilfer fractional derivative operator. It is general enough to include many different useful types of fractional calculus. We emphasised the power and importance of the conjugation relations. Mapping and limit properties of tempered Ψ -fractional operators. Existence, uniqueness, well-posedness, and stability for tempered Ψ -Hilfer FDEs.