Higher Order Fractal Differential Equations

Abstract

This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-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 $\alpha$-order linear fractal differential equations is defined, showcasing its non-integer dimensionality. The solutions to $\alpha$-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.