Numerical and analytical study of fractional hyperbolic equations with ψ -Caputo derivatives
Abstract
Abstract This paper presents a novel approach to address the Cauchy problem associated with fractional semilinear hyperbolic equations of order α ∈ (1, 2), encompassing various fractional derivatives. We introduce a priori assumptions on the solution and propose the Fourier truncation method to address the ill-posedness typically associated with such problems. Additionally, we establish a stability estimate characterized by logarithmic behavior. The theoretical findings are substantiated through numerical simulations, demonstrating the effectiveness of the proposed method.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Differential Equations and Boundary Problems
Numerical methods in inverse problems
Publication details
- Journal / source
- Journal of Nonlinear Complex and Data Science
- Publisher
- Walter de Gruyter GmbH
- Volume
- 27
- Issue
- 1
- Pages
- 17–41
- Publication date
- 21 January 2026
- Language
- EN