Cauchy problem in nonlocal statement for a system of fractional partial differential equations

We study the system $D_{0y}^alpha u_i + ( - 1)^{i - 1} lambda frac{partial } {{partial x}}u_i = a_{i1} u_1 + a_{i2} u_2 + f_i $D_{0y}^alpha u_i + ( - 1)^{i - 1} lambda frac{partial } {{partial x}}u_i = a_{i1} u_1 + a_{i2} u_2 + f_i , i = 1, 2, of Riemann-Liouville fractional partial differential equations with constant coefficients and prove theorems on the existence and uniqueness of a solution of a Cauchy problem in nonlocal statement.