Dumitru Baleanu1,2
1Department of Mathematics, Cankaya University, Ankara, Turkey
2Institute of Space Sciences, Magurele-Bucharest, Romania
Abstract– Fractional calculus deals with the investigation of the fractional-order integral and derivative operators over real or complex domains, and their applications. However, the physical meaning of the fractional operators is still an interesting open problem within this emerging field. In my talk, I will present the existing suggested physical interpretations of the fractional operators. Besides, I will consider the mechanism of a memory effect based on linear or non-linear systems of balance equations. By taking into account a chain of balance equations, connecting each particle to the next by means of a memory kernel, we can derive the generalized expressions for the overall memory kernel that connects the initial particle to the last particle. Also, by considering a general type of fractional integral operator to describe each balance equation, we obtain an expression for the generalized memory, which yields a more general type of fractional integral operator based on multivariate series. The use of the physical meaning of the fractional operators will be discussed within the fractional modeling point of view. Some illustrative examples will be presented.