About the Role
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About the Company
Abstract: In this talk, we start with a discussion of origins of the general fractional integrals and derivatives with the Sonin kernels in the works by Abel and Sonin. Then some recent results regarding properties of the general Fractional Calculus operators with the Sonin kernels are presented. In particular, the first and the second fundamental theorems of Fractional Calculus for the general fractional derivatives, the regularized general fractional derivatives, and the sequential general fractional derivatives are formulated. As an application, we discuss the convolution series that are a far-reaching generalization of the power law series as well as a representation of functions in form of the convolution Taylor series. Another application is the generalized convolution Taylor formula that contains a convolution polynomial and a remainder in terms of the general fractional integrals and the general fractional sequential derivatives. Finally, we provide a survey of some other recent results devoted to the general Fractional Calculus operators with the Sonin kernels and their applications.