An Inverse Problem for an Evolution Equation with a Time Fractional Derivative of Order α ∈ (1, 2) Involving LeGendre Polynomials

Mohammed Elamine Beroudj; Mokhtar Kirane; Abdelaziz Mennouni

doi:10.3934/dcdss.2025018

An Inverse Problem for an Evolution Equation with a Time Fractional Derivative of Order α ∈ (1, 2) Involving LeGendre Polynomials

Mohammed Elamine Beroudj
, Mokhtar Kirane
, Abdelaziz Mennouni

Mathematics

University of Batna

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This study aims to investigate an inverse problem related to a fractional partial differential equation of order α ∈ (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.

Original language	British English
Pages (from-to)	81-98
Number of pages	18
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	23
DOIs	https://doi.org/10.3934/dcdss.2025018
State	Published - 12 Mar 2026

Keywords

Caputo fractional derivative
Hilbert space
Inverse problem
involution
Legendre polynomials
partial differential equation
series expansion
spectral problem

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10.3934/dcdss.2025018

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title = "An Inverse Problem for an Evolution Equation with a Time Fractional Derivative of Order α ∈ (1, 2) Involving LeGendre Polynomials",

abstract = "This study aims to investigate an inverse problem related to a fractional partial differential equation of order α ∈ (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.",

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AU - Beroudj, Mohammed Elamine

AU - Kirane, Mokhtar

AU - Mennouni, Abdelaziz

PY - 2026/3/12

Y1 - 2026/3/12

N2 - This study aims to investigate an inverse problem related to a fractional partial differential equation of order α ∈ (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.

AB - This study aims to investigate an inverse problem related to a fractional partial differential equation of order α ∈ (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.

KW - Caputo fractional derivative

KW - Hilbert space

KW - Inverse problem

KW - involution

KW - Legendre polynomials

KW - partial differential equation

KW - series expansion

KW - spectral problem

UR - https://www.scopus.com/pages/publications/105033687010

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DO - 10.3934/dcdss.2025018

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JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

ER -

An Inverse Problem for an Evolution Equation with a Time Fractional Derivative of Order α ∈ (1, 2) Involving LeGendre Polynomials

Abstract

Keywords

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