Subordination Principle for a Class of Fractional Order Differential Equations
Subordination Principle for a Class of Fractional Order Differential Equations
The fractional order differential equation \(u'(t)=Au(t)+\gamma D_t^{\alpha} Au(t)+f(t), \ t>0\), \(u(0)=a\in X\) is studied, where \(A\) is an operator generating a strongly continuous one-parameter semigroup on a Banach space \(X\), \(D_t^{\alpha}\) is the Riemann–Liouville fractional derivative of order \(\alpha \in (0,1)\), \(\gamma>0\) and \(f\) is an \(X\)-valued function. Equations of …