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A Cauchy Problem for Some Local Fractional Abstract Differential Equation with Fractal Conditions
J. APPLIED FUNCTIONAL ANALYSIS (2013)
  • Yang Xiaojun
  • Zhong Weiping
  • Gao Feng
Abstract

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.

Keywords
  • Fractional analysis,
  • local fractional differential equation,
  • generalized Banach space,
  • local fractional functional analysis
Publication Date
2013
Publisher Statement
This paper is coprighted by the publisher.
Citation Information
W.P. Zhong, X.J. Yang, F. Gao, A Cauchy problem for some local fractional abstract differential equation with fractal conditions, In Proc: AMAT 2012, accepted.