Fractional Differential Calculus Via Fractional Difference Theory and Applications

Contrary to most books on fractional calculus which start with definitions of fractional derivatives in terms of integrals, here one uses a definition expressed as the limit of fractional difference, what allows us to expand the theory step by step exactly like with Leibniz calculus, by handling infinitely small increments. It follows that the physical significance of this calculus sticks to real problems and that, as a result, it is quite suitable (perhaps excellent) in systems modeling. Physical increments have a parlance in modeling which one can find in our fractional calculus, but is nowhere in the definition of fractional derivative via integrals. Last but not least, the book deals with non-differentiable functions, whilst most classical approaches to fractional calculus refer to the Caputo definition which deals with differentiable functions.