On the \(\Phi\)-Hilfer iterative fractional differential equations

Shruti A. Kalloli; José Vanterler da C. Sousa; Kishor D. Kucche

doi:10.56754/0719-0646.2701.093

DOI:

https://doi.org/10.56754/0719-0646.2701.093

Abstract

To avoid studying iterative differential equations with distinct fractional order derivatives it is essential to treat them with a broad fractional derivative, which leaves other fractional derivatives as a special case. In this way, we study an initial value problem for non linear iterative fractional differential equations involving \(\Phi\)-Hilfer fractional derivative. We establish the existence and uniqueness of the solution through fixed point theorems. We prove results concerning the dependence of solution and Ulam-Hyers stability of the problem. Finally, we present an example for illustration to demonstrate our outcome.

Keywords

Iterative fractional differential equation , Φ-Hilfer derivative , fixed point theorems , existence and uniqueness , data dependency , Ulam-Hyers stability

Mathematics Subject Classification:

26A33 , 34A12 , 34K20 , 47H10

Shruti A. Kalloli Department of Mathematics, Shivaji University, Kolhapur-416 004, Maharashtra, India. https://orcid.org/0009-0002-5162-7316
José Vanterler da C. Sousa Aerospace Engineering, PPGEA-UEMA Department of Mathematics, DEMATI-UEMA São Luís, MA 65054, Brazil. https://orcid.org/0000-0002-6986-948X
Kishor D. Kucche Department of Mathematics, Shivaji University, Kolhapur-416 004, Maharashtra, India. https://orcid.org/0000-0002-7141-330X

Pages: 93–117
Date Published: 2025-04-30
Vol. 27 No. 1 (2025)

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INSPIRE program (DST/ INSPIRE Fellowship / 2020 / IF200482)
Science and Engineering Research Board (SERB) - Research Grant (Ref: File no. EEQ/2023/000843).