New Generalized Results for Modified Atangana-Baleanu Fractional Derivatives and Integral Operators

Authors

  • Gauhar Rahman Hazara university
  • Muhammad Samraiz University of Sargodha
  • Cetin Yildiz
  • Thabet Abdeljawad
  • Manar A. Alqudah Princess Nourah bint Abdulrahman University
  • Aiman Mukheimer Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i1.5697

Keywords:

Mittang--Leffler function, C-F fractional derivative;, Integral Transform, Laplace Transform, Differential Equations

Abstract

In this current study, first we establish the modified power Atangana-Baleanu fractional derivative operators (MPC) in both the Caputo and Riemann-Liouville (MPRL) senses. Using the convolution approach and Laplace transformation, the so-called modified power fractional Caputo and R-L derivative operators with non-singular kernels are introduced. We establish the
boundedness of the modified Caputo fractional derivative operator in this study. The fractional differential equations are solved with the generalised Laplace transform (GLT). In addition, the corresponding form of the fractional integral operator is defined. Also, we prove the boundedness and Laplace transform of the fractional integral operator. The composition of power fractional
derivative and integral operators is given in the study. Additionally, several examples related to our findings along with their graphical representation are presented.

Author Biographies

  • Gauhar Rahman, Hazara university

    Department of Mathematics & Statistics

    Assistant Professor

  • Manar A. Alqudah, Princess Nourah bint Abdulrahman University

    Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi

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Published

2025-01-31

Issue

Vol. 18 No. 1: (January 2025)

Section

Nonlinear Analysis

License

Copyright (c) 2025 Gauhar Rahman, Muhammad Samraiz, Cetin Yildiz, Thabet Abdeljawad, Manar A. Alqudah

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How to Cite

New Generalized Results for Modified Atangana-Baleanu Fractional Derivatives and Integral Operators. (2025). European Journal of Pure and Applied Mathematics, 18(1), 5697. https://doi.org/10.29020/nybg.ejpam.v18i1.5697