General ((k,p),ψ)-Hilfer fractional integrals

Benaissa, Bouharket and Budak, Huseyin (2024) General ((k,p),ψ)-Hilfer fractional integrals. Miskolc Mathematical Notes, 25 (2). pp. 617-627. ISSN 1787-2413

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Abstract

The main motivation of this study is to establish a general version of the Riemann-Liouville fractional integrals with two exponential parameters k and p called ((k,p),ψ)-Hilfer fractional integrals which is determined over the k-gamma function. We first prove that these operators are well-defined, continuous and have semi-group property. Then, particularly, we present the harmonic, geometric and arithmetic (k,p),ψ-Hilfer fractional integrals. Moreover, some special cases relating to general ((k,p),ψ)-Riemann-Liouville fraction integrals are given.

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