Search

Abstract In this report we establish Green's formula for an integro-differential operator, and apply it to describe a class of self-adjoint fractional order differential operators. A found symmetric fractional order Caputo–Riemann–Liouville type operator can be considered as a fractional analogue of the classical Sturm–Liouville operator in some sense. [ABSTRACT FROM AUTHOR]

The present work studies the effect of an impulsive perturbation to classical and fractional classes of initial value problems. Scattering properties of the time sequences corresponding to the impulses are studied in the both integer and non-integer order cases. It is shown that, the sign-changing property of the perturbation function determines the mentioned scattering property of the kick times. [ABSTRACT FROM AUTHOR]

We propose a simple and accurate numerical scheme for solving the time fractional telegraph (TFT) equation within Caputo type fractional derivative. A fictitious coordinate ϑ is imposed onto the problem in order to transform the dependent variable u ( x , t ) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of method of line and group preserving scheme (GPS) is proposed to find the approximate solutions. This method preserves the geometric structure of the problem. Power and accuracy of this method has been illustrated through some examples of TFT equation. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional moving-boundary problem for the time-fractional diffusion equation, where the time-fractional derivative of order α ∈ ( 0 , 1 ) is taken in the Caputo sense. A generalization of the Hopf lemma is proved and then used to prove a monotonicity property for the free-boundary when a fractional free-boundary Stefan problem is investigated. [ABSTRACT FROM AUTHOR]