Tomáš Kisela

On Asymptotic Behaviour of Solutions of a Linear Fractional Differential Equation with a Variable Coefficient

abstract:
The paper deals with qualitative analysis of solutions of a test linear differential equation involving variable coefficient and derivative of non-integer order. We formulate upper and lower estimates for these solutions depending on boundedness of the variable coefficient. In the special case of asymptotically constant coefficient, we present the sufficient (and nearly necessary) conditions for the convergence of solutions to zero.

Mathematics Subject Classification: 34A08, 34K12, 34K20, 34K25

Key words and phrases: Fractional differential equation, variable coefficients, stability, asymptotic behaviour