Open Access. Powered by Scholars. Published by Universities.®
Ordinary Differential Equations and Applied Dynamics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 2 of 2
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun
Xiao-Jun Yang
The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.
A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng
A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng
Xiao-Jun Yang
Fractional calculus is an important method for mathematics and engineering [1-24]. In this paper, we review the existence and uniqueness of solutions to the Cauchy problem for the local fractional differential equation with fractal conditions \[ D^\alpha x\left( t \right)=f\left( {t,x\left( t \right)} \right),t\in \left[ {0,T} \right], x\left( {t_0 } \right)=x_0 , \] where $0<\alpha \le 1$ in a generalized Banach space. We use some new tools from Local Fractional Functional Analysis [25, 26] to obtain the results.