Work

Double Local Fractional Yang–Laplace Transform for Local Fractional PDEs on Fractal Domains

Year: 2025

Type: article

Abstract: This study introduces a novel analytical technique known as the double local fractional Yang–Laplace transform method (LFLζ2) and rigorously investigates its foundational properties, including linearity, differentiation, and convolution. The proposed method is formulated via double local fractional integrals, enabling a robust mechanism for addressing local fractional partial differential equations defined on fractal domains, particularly Cantor sets. Through a series of illustrative examples, we demonstrate the applicability and efficacy of the LFLζ2 transform in solving complex local fractional partial differential equation models. Special emphasis is placed on the local fractional Laplace equation, the linear local fractional Klein–Gordon equation, and other models, wherein the method reveals significant computational and analytical advantages. The results substantiate the method’s potential as a powerful tool for broader classes of problems governed by local fractional dynamics on fractal geometries.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9070434

Authors: Djelloul Ziane, Mountassir Hamdi Cherif, Carlo Cattani, Abdelhamid Mohammed Djaouti

Institutions: University of Ouargla, Ecole Supérieure en Génie Electrique et Energétique d'Oran, Università degli Studi della Tuscia, King Faisal University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Deanship of Scientific Research, King Faisal University