Operational Calculus for the General Fractional Derivative and Its Applications

In this paper, we first address the general fractional integrals and derivatives with Sonine kernels that possess integrable singularities of power function type at point zero. Both particular cases compositions these operators are discussed. Then proceed a construction an operational calculus Mikusi\'nski for kernels. This is applied analytical treatment some initial value problems differential equations derivatives. The solutions expressed in form convolution series generalize exponential Mittag-Leffler functions.