Fractal Differential Equations of 2<i>α</i>-Order

Abstract

In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a 2α-order fractal differential equation with constant coefficients across different scenarios. We propose a uniqueness theorem for 2α-order fractal linear differential equations. We define the solution space as a vector space with non-integer orders. We establish precise conditions for 2α-order fractal linear differential equations and derive the corresponding fractal adjoint differential equation.

Keywords

• fractal calculus
• 2α-order fractal linear differential equations
• fractal adjoint differential equation