A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

The minimum energy control problem of positive fractional-discrete time linear systems is addressed. Necessary and sufficient conditions for the reachability of the system are established. Sufficient conditions for the solvability of the minimum energy control of the positive fractional discrete-time systems are given. A procedure for computation of the optimal sequence of inputs minimizing the...

This paper presents a generalization of the Kalman Filter for linear and nonlinear fractional order discrete state-space systems. The linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified Kalman Filter for linear case is called Fractional Kalman Filter and its nonlinear extension is named Extended Fractional Kalman Filter respectively. The backgr...

This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background ...

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law nonlocality, power-law long-term memory or fractal properties by using integrations and differentiation of noninteger orders, i.e., by methods in the fractional calculus. This paper is a review of physical models that look very promising for futu...