Work

Higher order fractal differential equations

Year: 2024

Type: article

Abstract: This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with [Formula: see text]-order. Solutions for these equations with constant coefficients are obtained through the method of variation of parameters and the method of undetermined coefficients. The solution space for higher [Formula: see text]-order linear fractal differential equations is defined, showcasing its non-integer dimensionality. The solutions to [Formula: see text]-order linear fractal differential equations are graphically depicted to illustrate their non-differentiability. Additionally, equations of motion governing the behavior of two masses in fractal time are proposed and solved.

Source: Modern Physics Letters A

DOI: 10.1142/s021773232450127x

Authors: Alireza Khalili Golmankhaneh, Claude Depollier, Diana Pham

Institutions: Islamic Azad University of Urmia, Le Mans Université, The University of Texas at Arlington

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4402902772

FWCI: 2.781

Cites: 54

Cited by: 8

Related to: 10