An operator theoretical approach to a class of fractional order differential equations

We propose a general method to obtain 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 in case of the fractional order differential equation Dα t u (t) + µDα t u(t) = Au(t) + t−α Γ(1 − α) (u (0) + µu(0)) + f(t), t > 0, 0 < α ≤ 1, where A is an unbounded closed operator defined on a Banach space X and f is a X-valued function.

• Type: Journal
• Year: 2011
• Where: APPML
• Authors: Carlos Lizama
• Keywords: APPML 2011, Fractional Order, Linear Fractional Order, Order Differential Equation, Software Engineering