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A Cauchy Problem for Some Local Fractional Abstract Differential Equation with Fractal Conditions

Fractional calculus is an important method for mathematics and engineering . In this paper, we review the existence and uniqueness of solutions to the Cauchy problem for the local fractional di¤erential equation with fractal conditions D x (t) = f (t; x (t)) ; t 2 [0; T ] ; x (t0) = x0; where 0 < 1 in a generalized Banach space. We use some new tools from Local Fractional Functional Analysis [25, 26] to obtain the results.