An Operator Theoretical Approach to a Class of Fractional Order Differential Equations

We propose a general method for obtaining the representation of solutions for linear fractional order differential equations based on the theory of (a,k)-regularized families of operators. We illustrate the method for the case of the fractional order differential equation Dt?u?(t) +?Dt?u(t)=Au(t)+t-??(1-?)(u?(0)+?u(0))+f(t), t>0,0<??1,?