Smoothing noisy data with spline functions is well known in approximation theory. Smoothing splines have been used to deal with the problem of numerical differentiation. In this paper, we extend this method to estimate the fractional derivatives of a smooth signal from its discrete noisy data. We begin with finding a smoothing spline by solving the Tikhonov regularization problem. Then, we prop...

This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution. Keywords— Circuit Design, Fractional-Order Systems, Genetic Algorithms, Logic Circuits.

Iteration is involved in the fields of dynamical systems and numerical computation and so forth. The computation of iteration is difficult for general functions even for some simple functions such as linear fractional functions . In this paper, we discuss fractional polynomial function and use the method of conjugate similitude to obtain its expression of general iterate of order n under two di...

In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent...

Abstract In this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory further development and extension space-fractional (non-local) Euler–Bernoulli model (s-FEBB) to Timoshenko (s-FTB) one by proper taking into account shear deformation. Furthermore, detailed parametric study on influence le...

This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution. Keywords— Circuit Design, Fractional-Order Systems, Genetic Algorithms, Logic Circuits.

The exact stability condition for certain class of fractional-order multivalued transfer functions is presented. Unlike the conventional case that the stability is directly studied by investigating the poles of the transfer function, in the systems under consideration, the branch points must also come into account as another kind of singularities. It is shown that a multivalued transfer functio...

In this paper, the computation of a fractional derivative using the Fourier transform and a digital FIR di!erentiator is investigated. First, the Cauchy integral formula is generalized to de"ne the fractional derivative of functions. Then the fractional di!erentiation property of the Fourier transform of functions is presented. Using this property, the fractional derivative of a function can be...