With the increasing importance of Mittag-Leffler function in physical applications, these days many researchers are studying various generalizations and extensions function. In this paper efforts made to define bicomplex extension also its analyticity region convergence discussed. Various properties including integral representation, recurrence relations, duplication formula differential relati...

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the boun...

We study the combined effects of noise and detector sensitivity on a dynamical process that generates intermittent events mimicking the behavior of complex systems. By varying the sensitivity level of the detector we move between two forms of complexity, from inverse power law to Mittag-Leffler interevent time survival probabilities. Here fluctuations fight against complexity, causing an expone...

This article aims to examine Jeffery nanofluid with joint effects of mass and heat transfer in a horizontal channel. The classical model is transferred the Caputo fractional by using generalized Fourier’s Fick’s laws. nanofluids are formed dispersing two different nanoparticles, silver copper, into based fluid. A novel transformation has been applied energy equation then solved sine Fourier Lap...

A fractional model of the Hopfield neural network is considered in case application generalized proportional Caputo derivative. The stability analysis this used to show reliability processed information. An equilibrium defined, which generally not a constant (different than ordinary derivatives and Caputo-type derivatives). We define exponential Mittag–Leffler equilibrium. For this, we extend s...