Solving a time-fractional semilinear hyperbolic equations by Fourier truncation with boundary conditions

Abdelmjid Benmerrous, Fatima Ezzahra Bourhim, Ali El Mfadel and Elomari, M’hamed

Chaos, Solitons & Fractals, 2024, vol. 185, issue C

Abstract: In this paper, we discuss a pioneering contribution in the field by addressing, for the first time, the Cauchy problem associated with fractional semilinear hyperbolic equations of order α∈(1,2), involving a general form of fractional derivative. Introducing an a priori assumption on the solution, we advocate the application of the Fourier truncation method to address the inherent ill-posed nature of the problem. Furthermore, we establish a stability estimate of logarithmic type.

Keywords: Semilinear hyperbolic equations; Fourier truncation method; Estimation; Fixed point theorems; Banach space (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924006386

DOI: 10.1016/j.chaos.2024.115086

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