On ψ-Hilfer generalized proportional fractional operators

AIMS Mathematics

Ishfaq Mallah¹  Idris Ahmed²  Ali Akgul³  Fahd Jarad⁴ 

[1] 1. Department of Mathematics, Maulana Azad National Urdu University Gachibowli, Hyderabad-500032, India;2. Department of Mathematics, Sule Lamido University, P. M. B 048 Kafin Hausa, Jigawa State, Nigeria;3. Department of Mathematics, Art and Science Faculty, Siirt University, TR-56100 Siirt, Turkey;4. Department of Mathematics, Cankaya University, 06790 Etimesgut, Ankara, Turkey 5. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;

关键词: hilfer fractional derivative;    generalized proportional fractional derivative;    existence and uniqueness;    weighed space;    fixed point theorems;   

DOI  :  10.3934/math.2022005

来源: DOAJ

【 摘 要 】

In this paper, we introduce a generalized fractional operator in the setting of Hilfer fractional derivatives, the ψ-Hilfer generalized proportional fractional derivative of a function with respect to another function. The proposed operator can be viewed as an interpolator between the Riemann-Liouville and Caputo generalized proportional fractional operators. The properties of the proposed operator are established under some classical and standard assumptions. As an application, we formulate a nonlinear fractional differential equation with a nonlocal initial condition and investigate its equivalence with Volterra integral equations, existence, and uniqueness of solutions. Finally, illustrative examples are given to demonstrate the theoretical results.

【 授权许可】

Unknown