Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Analysis and design of fractional-order digital control systems
Systems Analysis Modelling Simulation
Editorial: fractional signal processing and applications
Signal Processing - Special issue: Fractional signal processing and applications
On the initial conditions in continuous-time fractional linear systems
Signal Processing - Special issue: Fractional signal processing and applications
A new IIR-type digital fractional order differentiator
Signal Processing - Special issue: Fractional signal processing and applications
An explicit and numerical solutions of the fractional KdV equation
Mathematics and Computers in Simulation
Fractional calculus applications in signals and systems
Signal Processing - Fractional calculus applications in signals and systems
A coherent approach to non-integer order derivatives
Signal Processing - Fractional calculus applications in signals and systems
A new least-squares approach to differintegration modeling
Signal Processing - Fractional calculus applications in signals and systems
An approximate method for numerical solution of fractional differential equations
Signal Processing - Fractional calculus applications in signals and systems
Fractional system identification for lead acid battery state of charge estimation
Signal Processing - Fractional calculus applications in signals and systems
Solving a system of nonlinear fractional differential equations using Adomian decomposition
Journal of Computational and Applied Mathematics
An efficient method for solving systems of fractional integro-differential equations
Computers & Mathematics with Applications
Numerical approach to differential equations of fractional order
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
ETFA'09 Proceedings of the 14th IEEE international conference on Emerging technologies & factory automation
System initial conditions vs derivative initial conditions
Computers & Mathematics with Applications
Approximate analytical solution to fractional modified KdV equations
Mathematical and Computer Modelling: An International Journal
Journal of Computational and Applied Mathematics
Fractional zero-phase filtering based on the Riemann-Liouville integral
Signal Processing
| Hi-index | 0.08 |
A look into fractional calculus and its applications from the signal processing point of view is done in this paper. A coherent approach to the fractional derivative is presented, leading to notions that are not only compatible with the classic but also constitute a true generalization. This means that the classic are recovered when the fractional domain is left. This happens in particular with the impulse response and transfer function. An interesting feature of the systems is the causality that the fractional derivative imposes. The main properties of the derivatives and their representations are presented. A brief and general study of the fractional linear systems is done, by showing how to compute the impulse, step and frequency responses, how to test the stability and how to insert the initial conditions. The practical realization problem is focussed and it is shown how to perform the input-ouput computations. Some biomedical applications are described.