Shantanu Das

Bio: Shantanu Das is an academic researcher from Bhabha Atomic Research Centre. The author has contributed to research in topics: Fractional calculus & PID controller. The author has an hindex of 24, co-authored 152 publications receiving 2925 citations. Previous affiliations of Shantanu Das include University of Chicago & Jadavpur University.

Chaos Synchronization in Commensurate Fractional Order Lü System via Optimal PIλ Dμ Controller with Artificial Bee Colony Algorithm

Abstract: In this paper a master-slave approach to chaos synchronization in commensurate fractional order FO Lu system has been studied via optimally designed fractional order Proportional Integral Derivative PID Controller. An optimization frame work based on integral time indices has been considered for tuning the unknown parametric constants of FOPID controller. The optimization task was carried out using bees swarm intelligent based Artificial Bee Colony algorithm. A comparative study based on conventional PID control scheme has also been performed to highlight the advantage of using fractional order controller for fractional order systems. Simulation results presented for synchronization of chaos in two Lu systems supports the claim for proposed approach.

Analytical Solution with Tanh-Method and Fractional Sub-Equation Method for Non-Linear Partial Differential Equations and Corresponding Fractional Differential Equation Composed With Jumarie Fractional Derivative

Abstract: The solution of non-linear differential equation, non-linear partial differential equation and non-linear fractional differential equation is current research in Applied Science. Here tanh-method and Fractional Sub-Equation methods are used to solve three non-linear differential equations and the corresponding fractional differential equation. The fractional differential equations here are composed with Jumarie fractional derivative. Both the solution is obtained in analytical traveling wave solution form. We have not come across solutions of these equations reported anywhere earlier.

Functions Used in Fractional Calculus

Abstract: This chapter presents a number of functions that have been found useful in the solution of the problems of fractional calculus. The base function is the Gamma function, which generalizes the factorial expression, used in multiple differentiation and repeated integrations, in integer order calculus. The Mittag-Leffler function is the basis function of fractional calculus, as exponential function is to integer order calculus. Several modifications of the Mittag-Leffler functions, along with other variants are introduced which are developed since 1903, for study of the fractional calculus. These functions are called Higher Transcendental Functions and its use in solving Fractional Differential Equations is as similar to use of transcendental functions for solving Integer Order Differential Equations. Use of these functions is demonstrated for solving Fractional differential equations with Laplace Transform Technique. Here, some interesting physical interpretation is given, for memory integrals for relaxation laws for generalized system dynamics (with memory); along with basic definition and physical interpretation of rough functions, and its fractal dimension. Several examples are solved to get fractional integration and fractional differentiation of standard function and use of introduced higher transcendental functions is demonstrated especially for solving Fractional Differential Equations.

Quenching the conducted emission hazards for heliborne time domain electromagnetic exploration system

Abstract: Noise limits set by regulatory agencies make solutions to common mode EMI a necessary consideration in the manufacture and use of electronic equipment. Common mode filters are generally relied upon to suppress line conducted common mode interference. These filters successfully and reliably reduce common mode noise. However, successful design of common mode filters requires foresight into the non ideal character of filter components - the inductor in particular. It is the aim of this paper to provide filter designers the knowledge required to identify those characteristics critical to desired filter performance.

Ultracapacitors: Why, How, and Where is the Technology

Abstract: The science and technology of ultracapacitors are reviewed for a number of electrode materials, including carbon, mixed metal oxides, and conducting polymers. More work has been done using microporous carbons than with the other materials and most of the commercially available devices use carbon electrodes and an organic electrolytes. The energy density of these devices is 3¯5 Wh/kg with a power density of 300¯500 W/kg for high efficiency (90¯95%) charge/discharges. Projections of future developments using carbon indicate that energy densities of 10 Wh/kg or higher are likely with power densities of 1¯2 kW/kg. A key problem in the fabrication of these advanced devices is the bonding of the thin electrodes to a current collector such the contact resistance is less than 0.1 cm2. Special attention is given in the paper to comparing the power density characteristics of ultracapacitors and batteries. The comparisons should be made at the same charge/discharge efficiency.

Multi-index Mittag-Leffler Functions

Abstract: Consider the function defined for \(\alpha _{1},\ \alpha _{2} \in \mathbb{R}\) (α 1 2 +α 2 2 ≠ 0) and \(\beta _{1},\beta _{2} \in \mathbb{C}\) by the series $$\displaystyle{ E_{\alpha _{1},\beta _{1};\alpha _{2},\beta _{2}}(z) \equiv \sum _{k=0}^{\infty } \frac{z^{k}} {\varGamma (\alpha _{1}k +\beta _{1})\varGamma (\alpha _{2}k +\beta _{2})}\ \ (z \in \mathbb{C}). }$$ (6.1.1) Such a function with positive α 1 > 0, α 2 > 0 and real \(\beta _{1},\beta _{2} \in \mathbb{R}\) was introduced by Dzherbashian [Dzh60].