loading page

Existence and Uniqueness Results for Hilfer-Generalized Proportional Derivatives with Nonlocal Conditions
  • Thumbnail
  • +2
  • Idris AhmedOrcid,
  • Poom Kumam,
  • Fahd Jarad,
  • Piyachat Borisut,
  • Wachirapong Jirakitpuwapat
Idris Ahmed
Orcid
King Mongkut's University of Technology Thonburi
Author Profile
Medium
Poom Kumam
King Mongkut's University of Technology Thonburi
Author Profile
Fahd Jarad
Cankaya Universitesi
Author Profile
Piyachat Borisut
King Mongkut’s University of Technology Thonburi (KMUTT)
Author Profile
Wachirapong Jirakitpuwapat
King Mongkut's University of Technology Thonburi
Author Profile

Abstract

In this paper, motivated by Hilfer and Hilfer-Katugampola fractional derivatives, we introduce new Hilfer-generalized proportional derivatives which interpolate the classical fractional derivatives of Hilfer, Riemann-Liouville, Caputo and generalized proportional fractional derivatives. We also present some important properties of the proposed derivatives. Furthermore, as an application, we show that this equation is equivalent to the Volterra integral equation and prove the existence, uniqueness of the solution to the Cauchy problem with the nonlocal initial condition. Finally, two examples were given to illustrate the results.