In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

In this paper we present a new technique to compute non-dominated solutions, with an error that can be made as low as the user wants, in multiple objective linear fractional programming (MOLFP), using reference points. The basic idea is to divide, by the approximate ‘middle’, the non-dominate region in two sub-regions and to analyze each of them in order to try to discard one. The process is re...

In this paper, the perturbed Gerdjikov–Ivanov (GI) equation using a truncated M-fractional derivative is studied in mathematical nonlinear optics. We are explored its novel dark and other soliton solutions compared them with existing results. To obtain objective, two particular methods, modified extended $$\tanh$$ expansion method $$Exp_a$$ function method, implemented. exercise, an arrangement...

BACKGROUND Normal values for regional left ventricular wall motion, although documented in adults, have not been reported in healthy newborns. METHODS This study prospectively evaluated global and segmental systolic and diastolic cardiac function by color kinesis in clinically asymptomatic healthy newborns. RESULTS Eighty-eight asymptomatic infants who were less than 48 hours old were studi...

Digital filters capable of changing their frequency response characteristics are often referred to as variable digital filters (VDF’s) and have been found useful in a number of digital signal processing applications. An important class of VDF’s is the class of digital filters with variable fractional delay. This paper describes an enhanced weighted least-squares design for variable-fractional-d...

Abstract. We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard–Marchaud fractional derivative, is also considered. The objective is to represent these operators as series of terms involving integer-order derivatives only, and then approximate the fractional operators by a finite sum. An upper bound ...

The previous work in [1], Tseng et al. have designed a fractional order differentiator using radial basis function by directly truncating the coefficients to approximate the fractional order derivative Dα of the given digital signal. This paper presents the designing of fractional order differentiator using radial basis function and window. Three design examples are given to illustrate that the...

In this paper, based on certain variable transformation, we apply the known (G’/G) method to seek exact solutions for three fractional partial differential equations: the space fractional (2+1)-dimensional breaking soliton equations, the space-time fractional Fokas equation, and the spacetime fractional Kaup-Kupershmidt equation. The fractional derivative is defined in the sense of modified Rie...