In this work, we introduce a generalization of the differential polynomial neural network utilizing fractional calculus. Fractional calculus is taken in the sense of the Caputo differential operator. It approximates a multi-parametric function with particular polynomials characterizing its functional output as a generalization of input patterns. This method can be employed on data to describe m...

We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on particular yet relevant case, for which provide several ready-for-use combinatorial identities, including an adapted version the Pascal's rule. then investigate associated generating functions, establish recursive, and integral formulation. From this, derive asym...

The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiat...

Fractional calculus and fractional differential equations are popular in describing anomalous diffusion, ground water flow and transport, and the price fluctuation in finance, etc. Some numerical methods are developed to solve the fractional ordinary differential equations. However, for most of these methods it seems that we always have to make a trade-off between efficiency and accuracy becaus...

Local fractional calculus (fractal calculus) plays a crucial role in applications, especially computer sciences and engineering. One of these applications appears the theory chaos. Therefore, this paper studies dynamics fractal complex logistic map then employs to generate chaotic sequences for new symmetric image encryption algorithm. Firstly, we derive investigate its by determining equilibri...

Fractional differential calculus have recently been addressed by many researchers of various fields of science and engineering such as physics, chemistry, biology, economics, control theory, and biophysics, etc. [1-4]. In particular, the existence of solutions to fractional boundary value problems is under strong research recently, see [5-7] and references therein. The fractional q-difference c...

In this paper, a new theory of generalized micropolar thermoelasticity is derived by using fractional calculus. The generalized heat conduction equation in micropolar thermoelasticity has been modified with two distinct temperatures, conductive temperature and thermodynamic temperature by fractional calculus which depends upon the idea of the RiemannLiouville fractional integral operators. A un...