in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

First order plus time delay model is widely used to model systems with S-shaped reaction curve. Its generalized form is the use of a single fractional pole to replace the first order (singletime constant) model, which is believed to better characterize the reaction curve. Using time delayed system model with a fractional pole as the starting point, in this paper, designing fractional order cont...

In this note, we study the stability and controller robustness of some popular proportional-integral-derivative (PID) tuning techniques that are based on first-order models with time delays. Using the characterization of all stabilizing PID controllers derived in a previous paper, each tuning rule is analyzed to first determine if the proportional gain value dictated by that rule, lies inside t...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

A fractional order (FO) PID or FOPID controller is designed for an Automatic Voltage Regulator (AVR) system with the consideration of contradictory performance objectives. An improved evolutionary Nondominated Sorting Genetic Algorithm (NSGA-II), augmented with a chaotic Henon map is used for the multiobjective optimization based design procedure. The Henon map as the random number generator ou...

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...