10.57647/j.jtap.2025.1905.52

The time wave equation with new conformable fractional derivative definition

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  • Abdessamad Ait Brahim*1,
  • Abdelmajid El Hajaji2,
  • Khalid Hilal1,
  1. AMSC Laboratory, University of Sciences and Technology , Beni Mellal, Morocco
  2. OEE Departement, ENCGJ, University of Chouaib Doukali, El jadida, Morocco

Received: 2025-01-26

Revised: 2025-02-15

Accepted: 2025-06-27

Published in Issue 2025-09-30

Copyright (c) 2025 Abdessamad Ait Brahim, Abdelmajid El Hajaji, Khalid Hilal (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
Brahim AA, El Hajaji A, Hilal K. The time wave equation with new conformable fractional derivative definition. J Theor Appl phys. 2025 Sep. 30;19(5). Available from: https://oiccpress.com/jtap/article/view/17964
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Abstract

 This study employs a novel approach to solving two and three-dimensional time fractional wave equations by
 utilizing the new results of fractional derivative definition, with a particular focus on the newly introduced
 “New conformable fractional derivative” as outlined in [1]: 
 DNβ​(t)=h→0lim​hN(t+he(β−1)t)−N(t)​,β∈[0,1)
 where N : [0,∞) →R a function and β ∈[0,1). This definition offers simplicity and high effectiveness in
 addressing fractional differential equations with complex solutions, surpassing traditional fractional derivative
 definitions such as Caputo and Riemann-Liouville. Our findings indicate that the new conformable fractional
 derivative definition is both practical and efficient for resolving higher-dimensional fractional differential
 equations.

Keywords

  • Fractional wave equation,
  • New conformable fractional derivative
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