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

Author

Listed:
  • Benmerrous, Abdelmjid
  • Bourhim, Fatima Ezzahra
  • El Mfadel, Ali
  • Elomari, M’hamed

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.

Suggested Citation

  • Benmerrous, Abdelmjid & Bourhim, Fatima Ezzahra & El Mfadel, Ali & Elomari, M’hamed, 2024. "Solving a time-fractional semilinear hyperbolic equations by Fourier truncation with boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924006386
    DOI: 10.1016/j.chaos.2024.115086
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