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article · Discrete and Continuous Dynamical Systems - S

An inverse problem for an evolution equation with a time fractional derivative of order <inline-formula><tex-math id="M1">$ \alpha \in (1, \, 2) $</tex-math></inline-formula> involving Legendre polynomials

20251 citationOpen accessUniversity of Batna 1

Abstract

This study aims to investigate an inverse problem related to a fractional partial differential equation of order $\alpha \in (1, 2)$, associated with the Legendre differential equation. We first establish the existence and uniqueness of solutions. Using the Legendre orthogonal basis, we obtain solutions through a series expansion and analyze the convergence of this expansion.

Research topics

  • Fractional Differential Equations Solutions
  • Numerical methods in inverse problems
  • Differential Equations and Boundary Problems

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DOI: 10.3934/dcdss.2025018

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