Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electric...

We study a particular number pyramid bn,k,l that relates the binomial, Deleham, Eulerian, MacMahon-type and Stirling number triangles. The numbers bn,k,l are generated by a function Bc(x, y, t), c ∈ C, that appears in the calculation of derivatives of a class of functions whose derivatives can be expressed as polynomials in the function itself or a related function. Based on the properties of t...

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We study Taylor series expansions of stationary characteristics of general-state-space Markov chains. The elements of the Taylor series are explicitly calculated and a lower bound for the radius of convergence of the Taylor series is established. The analysis provided in this paper applies to the case where the stationary characteristic is given through an unbounded sample performance function ...

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Tayl...

Current speaker diarization systems typically fail to successfully assign multiple speakers speaking simultaneously. According to previous studies, overlapping errors account for a large proportion of the total errors in multi-party speech diarization. In this work, we propose a new approach using Vector Taylor Series (VTS) to obtain overlapping speech models assuming individual speaker models ...

Abstract A generalized q-Taylor’s formula in fractional q-calculus is established and used in deriving certain q-generating functions for the basic hypergeometric functions and basic Fox’s H-function. 2010 Mathematics Subject Classification: 33D45, 26A33 and 33D90.

In view of a general formula for higher order derivatives the ratio two differentiable functions, authors establish first form Maclaurin power series expansion logarithmic expression in term determinants special Hessenberg matrices whose elements involve Bernoulli numbers. On other hand, comparison, recite and revise second terms Bessel zeta functions

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opin...