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...

We establish the correct solvability of a multipoint nonlocal (in time) problem for evolutionary equation with operator fractional differentiation and an initial function, which is element space generalized functions distribution type. The analytic representation solution presented. also analyze behavior in case unlimited growth time variable (stabilization solution).

The main goal of this article is to study the extend Struve and extended modified matrix functions by making use Beta function. In particular, we investigate certain important properties these such as integral representation, differentiation formula hypergeometric representation functions. Finally, obtain some results on transform fractional calculus

Fractional calculus is about the integration or differentiation of non-integer orders. The use of “fractional” is purely due to historical reasons [1]. Using fractional order differential equations is believed to be able to better characterize the nature around us. Using an integer order model is only for our own convenience. Depending on the scale on which we characterize the dynamics of a sys...

A fractional-order vascular model representation for emulating arterial hemody-namics has been recently presented as an alternative to the well-known integer-order Windkessel. The uses a capacitor (FOC) describe complex and frequency-dependent compliance. This paper presents two-stage algorithm based on modulating functions finite-time simultaneous estimation of model’s input fractional differe...

Fractional order calculus can represent systems with high-order dynamics and complex nonlinear phenomena using few coefficients, since the arbitrary order of the derivatives provides an additional degree of freedom to fit a specific behavior. Numerous mathematicians have contributed to the history of fractional calculus by attempting to solve a fundamental problem to the best of their understan...

In this work, variety of complex dynamics are found in a fractional-order antimicrobial resistance (AMR) model based on the generalized Gamma function. Firstly, extended left and right Caputo fractional differential operators, respectively, ELCFDO ERCFDO introduced. The basic features outlined. is shown to have new parameter that affects occurrence AMR system. Secondly, discretization studied u...

This paper examines the long-run dynamics and the cyclical structure of the US stock market using fractional integration techniques, specifically a version of the tests of Robinson (1994a) which allows for unit (or fractional) roots both at the zero (long-run) and at the cyclical frequencies. We consider inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio...

Fractional calculus, which deals with the integration and differentiation of non-integer order, is widely being used these days to mathematically model many engineering and scientific systems ranging from microbiological processes to astronomical images. The efficient and accurate analysis of such systems, usually referred to as the fractional order systems, has become very important and a numb...