GLOBAL-SOLUTIONS OF FRACTIONAL LINEAR-DIFFERENTIAL EQUATIONS

Processes and materials involving relaxation, creep and fading memory are better understood recently by using fractional LDE representations of the models for the advantage of reducing the number of parameters improving curve fitting schemes and avoiding nonlinearities. A mathema tical stringent method to define and solve such equations without an a -priori definition of fractional derivatives is presented. By establis hing a ''functional calculus'' we avoid the well-known difficulties su ch as fractional initial or boundary conditions and the loss of global ity. In particular, using the popular Fractional Calculus (see e.g. [3 ]) it is necessary to feed in casuality to get it out. In the case of constant coefficients we present criteria for existence, continuity an d causality of global solutions. Moreover we yet a surprisingly simple algorithm for obtaining the solutions.