fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order.the purpose of this work is to use hadamard fractional integral to establish some new integral inequalities of gruss type by using one or two parameters which ensues four main results . furthermore, other integral inequalities of reverse m...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

‎in this paper, we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor (pmsm) system. the necessary condition for the existence of chaos in the fractional-order pmsm system is deduced and an active controller is developed based on the stability theory for fractional systems. the presented control scheme  is simple and flexible, and it is suitable both fo...

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

Effluents of resin production, petrochemicals, refineries, paper mills, and iron foundry industries may present high concentrations of phenol. The high toxicity, solubility, and stability of phenolic compounds hamper the treatment of this wastewater by conventional methods. In this work, the effect of inorganic ion mixtures, such as chloride, nitrate, sulfate, carbonate, and monophosphate on th...

With reference to Lee’s treatment of quasi-probabilities, it is seen that the three phase space quasi-probabilities, known as the P-, Husimi and Wigner ones, plus other intermediate ones, generate a common, single Fisher thermodynamics, along the lines developed by Frieden et al. We explore some facets of such thermodynamics and encounter complementarity between two different kinds of Fisher in...

In this paper, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...