ON THE MITTAG-LEFFLER–HYERS–ULAM STABILITY OF PRABHAKAR FRACTIONAL DIFFERENTIAL EQUATIONS THROUGH FRACTIONAL FOURIER TRANSFORMS

Paper ID: EIJTEM_2026_13_4_32-46

Author's Name: D. S. Sumathi, K. Alagesan

Volume: 13

Issue: 4

Year: 2026

Page No: 32-46

Abstract:

This paper aims to study the stability of the linear and nonlinear fractional differential equations in Mittag-Leffler- Hyers- Ulam sense with Prabhakar derivative. By using the Fractional Fourier transform, we show that the introduced fractional differential equations are Mittag-Leffler Hyers- Ulam- is stable with Prabhakar derivative. Some examples are given to illustrate the main theoretical results.

Keywords: Fractional differential equation, Riemann derivative, Prabhakar fractional integral, Prabhakar fractional derivative, Mittag-Leffler function, Fractional Fourier transform

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