Fractional differential and integral operations and cumulative processes
  In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of traditional fractional calculus for describing complex systems is uncovered. The connection between complex physics with fractional differentiation and integration operations is established. 
Fevzi Buyukkilic, Zahide Ok Bayrakdar, Dogan Demirhan
cond-mat.stat-mech math-ph math.MP