2025/02/26 by Brahim, Abdessamad Ait, El Hajaji, Abdelmajid, Hilal, Khalid
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Nonlinear Differential Equations Analysis
paper · doi:10.57647/j.jtap.2025.1905.52
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→0limhN(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.