The Weighted Cauchy Type Problem and Cauchy Problem for the Linear Barbashin Integro-Differential Equations with Fractional Partial Derivative

We establish the existence and uniqueness conditions for the weighted Cauchy type problem and the Cauchy problem for the linear Barbashin integro-differential equation with fractional partial derivative of order 0 < α ≤ 1 in the sense of Riemann–Liouville and Caputo. Bibliography: 8 titles.