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...Introduction some problems fractional calculus and ewa girejko e pb edu pl faculty of computer science bialystok university technology poland march rutgers camden usa seminar in the derivatives integrals background its origins go back more to year conversation l hopital leibniz throught letters can meaning with integer order be generalized non orders de hospital what if n it will lead a paradox from which one day useful consequences drawn after that many famous mathematicians like j fourier h abel liouville b riemann others contributed development theory arbitrary took or less nished form by end xix century dierentiation may introduced several dierent ways grunw ald letnikov caputo miller ross for three centuries was developed as pure theoretical eld mathematics only last few decades turned out very various elds physics classic quantum mechanics thermodynamics etc chemistry biology economics engineering signal image processing control web site podlubny http people tuke sk igor fc resou...