Structure preserving computational technique for fractional order Schnakenberg model

Load frequency control (LFC) is considered to be the most important strategy in interconnected multi-area power systems for satisfactory operation and distribution. In order to transfer reliable power with acceptable quality, an LFC mechanism requires highly efficacy and intelligent techniques. In this paper, a novel hybrid fractional order fuzzy pre-compensated intelligent proportional-integral-derivative (PID) (FOFP-iPID) controller is proposed for the LFC of a realistic interconnected two-area power system. The proposed FOFP-iPID controller is incorporated into the power system as a secondary controller. In doing so, the parameters of the suggested FOFP-iPID controller are optimized using a more recent evolutionary computational technique called the Ant lion optimizer (ALO) algorithm utilizing an Integral of Time multiplied Absolute Error (ITAE) index. Simulation results demonstrated that the proposed FOFP-iPID controller achieves better dynamics performance under a wide variation of load perturbations. The supremacy of the proposed FOFP-iPID controller is demonstrated by comparing the results with some existing controllers, such as fractional order PID (FOPID) and fractional order intelligent PID (FOiPID) controllers for the identical system. Finally, the sensitivity analysis of the plant is examined and the simulation results showed that the suggested FOFP-iPID controller is robust and performs satisfactorily despite the presence of uncertainties.

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Structure Preserving Algorithm for Fractional Order Mathematical Model of COVID-19

Computers Materials & Continua ◽

10.32604/cmc.2022.013906 ◽

2022 ◽

Vol 71 (2) ◽

pp. 2141-2157

Author(s):

Zafar Iqbal ◽

Muhammad Aziz-ur Rehman ◽

Nauman Ahmed ◽

Ali Raza ◽

Muhammad Rafiq ◽

...

Keyword(s):

Mathematical Model ◽

Fractional Order ◽

Structure Preserving

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Two efficient computational technique for fractional nonlinear Hirota–Satsuma coupled KdV equations

Engineering Computations ◽

10.1108/ec-02-2020-0091 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Amit Prakash ◽

Vijay Verma

Keyword(s):

Fractional Order ◽

Linear Time ◽

Numerical Technique ◽

Error Function ◽

Computational Technique ◽

Content Type ◽

Coupled Equations ◽

Non Linear ◽

Homotopy Analysis ◽

Sumudu Transform

Purpose The purpose of this paper is to apply an efficient hybrid computational numerical technique, namely, q-homotopy analysis Sumudu transform method (q-HASTM) and residual power series method (RPSM) for finding the analytical solution of the non-linear time-fractional Hirota–Satsuma coupled KdV (HS-cKdV) equations. Design/methodology/approach The proposed technique q-HASTM is the graceful amalgamations of q-homotopy analysis method with Sumudu transform via Caputo fractional derivative, whereas RPSM depend on generalized formula of Taylors series along with residual error function. Findings To illustrate and validate the efficiency of the proposed technique, the authors analyzed the projected non-linear coupled equations in terms of fractional order. Moreover, the physical behavior of the attained solution has been captured in terms of plots and by examining the L2 and L∞ error norm for diverse value of fractional order. Originality/value The authors implemented two technique, q-HASTM and RPSM to obtain the solution of non-linear time-fractional HS-cKdV equations. The obtained results and comparison between q-HASTM and RPSM, shows that the proposed methods provide the solution of non-linear models in form of a convergent series, without using any restrictive assumption. Also, the proposed algorithm is easy to implement and highly efficient to analyze the behavior of non-linear coupled fractional differential equation arisen in various area of science and engineering.

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A collocation method for solving the fractional calculus of variation problems

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v35i1.26333 ◽

2017 ◽

Vol 35 (1) ◽

pp. 163

Author(s):

Mohammad Reza Ahmadi ◽

Mitra Nasiri

Keyword(s):

Fractional Calculus ◽

Collocation Method ◽

Fractional Order ◽

Computational Technique ◽

Algebraic Equations ◽

Calculus Of Variation ◽

Collocation Points ◽

Müntz Polynomials ◽

Linear And Nonlinear ◽

Fractional Calculus Of Variation

In this paper we use a family of Muntz polynomials and a computational technique based on the collocation method to solve the calculus variation problem. This approach is utilizedto reduce the solution of linear and nonlinear fractional order dierential equations to the solution of a system of algebraic equations. Thus we can obtain a good approximation evenby using a smaller of collocation points.

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An Efficient Computational Technique for Fractional Model of Generalized Hirota–Satsuma-Coupled Korteweg–de Vries and Coupled Modified Korteweg–de Vries Equations

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4046898 ◽

2020 ◽

Vol 15 (7) ◽

Cited By ~ 16

Author(s):

P. Veeresha ◽

D. G. Prakasha ◽

Devendra Kumar ◽

Dumitru Baleanu ◽

Jagdev Singh

Keyword(s):

Fractional Order ◽

Water Waves ◽

Initial Conditions ◽

Computational Method ◽

Computational Technique ◽

Suggested Technique ◽

The Future ◽

De Vries ◽

Fractional Models ◽

The Future Method

Abstract The aim of the present investigation to find the solution for fractional generalized Hirota–Satsuma coupled Korteweg–de-Vries (KdV) and coupled modified KdV (mKdV) equations with the aid of an efficient computational scheme, namely, fractional natural decomposition method (FNDM). The considered fractional models play an important role in studying the propagation of shallow-water waves. Two distinct initial conditions are choosing for each equation to validate and demonstrate the effectiveness of the suggested technique. The simulation in terms of numeric has been demonstrated to assure the proficiency and reliability of the future method. Further, the nature of the solution is captured for different value of the fractional order. The comparison study has been performed to verify the accuracy of the future algorithm. The achieved results illuminate that, the suggested computational method is very effective to investigate the considered fractional-order model.

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A spectral framework for the solution of fractional optimal control and variational problems involving Mittag–Leffler nonsingular kernel

Journal of Vibration and Control ◽

10.1177/1077546320974815 ◽

2020 ◽

pp. 107754632097481

Author(s):

Haniye Dehestani ◽

Yadollah Ordokhani

Keyword(s):

Optimal Control ◽

Fractional Derivative ◽

Fractional Order ◽

Lagrange Multiplier ◽

Caputo Fractional Derivative ◽

Variational Problems ◽

Computational Technique ◽

Operational Matrices ◽

Algebraic Equations ◽

Fractional Optimal Control

A new fractional-order Dickson functions are introduced for solving numerically fractional optimal control and variational problems involving Mittag–Leffler nonsingular kernel. The type of fractional derivative in the proposed problems is the Atangana–Baleanu–Caputo fractional derivative. In the process of the method, we use fractional-order Dickson functions and their properties to provide an accurate computational technique for calculating operational matrices, at first. Then, with the help of operational matrices and the Lagrange multiplier method, these problems are reduced to a system of algebraic equations. At last, to demonstrate the effectiveness of the new method, we enforce the proposed algorithm for several examples.

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Structure-preserving extremely low light image enhancement with fractional order differential mask guidance

Proceedings of the 2nd ACM International Conference on Multimedia in Asia ◽

10.1145/3444685.3446319 ◽

2021 ◽

Author(s):

Yijun Liu ◽

Zhengning Wang ◽

Ruixu Geng ◽

Hao Zeng ◽

Yi Zeng

Keyword(s):

Image Enhancement ◽

Fractional Order ◽

Low Light ◽

Structure Preserving ◽

Light Image

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Distributed Control in Multiple Dimensions: A Structure Preserving Computational Technique

IEEE Transactions on Automatic Control ◽

10.1109/tac.2010.2063230 ◽

2011 ◽

Vol 56 (3) ◽

pp. 516-530 ◽

Cited By ~ 16

Author(s):

Justin K. Rice ◽

Michel Verhaegen

Keyword(s):

Distributed Control ◽

Computational Technique ◽

Structure Preserving ◽

Multiple Dimensions

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Numerical Investigation of Chemical Schnakenberg Mathematical Model

Journal of Nanomaterials ◽

10.1155/2021/9152972 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Faiz Muhammad Khan ◽

Amjad Ali ◽

Nawaf Hamadneh ◽

Abdullah ◽

Md Nur Alam

Keyword(s):

Fractional Order ◽

General Scheme ◽

Nonlinear Partial Differential Equations ◽

Adomian Decomposition Method ◽

Oscillatory Behavior ◽

Biochemical Processes ◽

Proposed Model ◽

Adomian Decomposition ◽

Schnakenberg Model ◽

Caputo Differential Operator

Schnakenberg model is known as one of the influential model used in several biological processes. The proposed model is an autocatalytic reaction in nature that arises in various biological models. In such kind of reactions, the rate of reaction speeds up as the reaction proceeds. It is because when a product itself acts as a catalyst. In fact, model endows fractional derivatives that got great advancement in the investigation of mathematical modeling with memory effect. Therefore, in the present paper, the authors develop a scheme for the solution of fractional order Schnakenberg model. The proposed model describes an auto chemical reaction with possible oscillatory behavior which may have several applications in biological and biochemical processes. In this work, the authors generalized the concept of integer order Schnakenberg model to fractional order Schnakenberg model. We provided the approximate solution for the underlying generalized nonlinear Schnakenberg model in the sense of Caputo differential operator via Laplace Adomian decomposition method (LADM). Furthermore, we established the general scheme for the considered model in the form of infinite series by the aforementioned technique. The consequent results obtained by the proposed technique ensure that LADM is an effective and accurate techniques to handle nonlinear partial differential equations as compared to the other available numerical techniques. Finally, the obtained numerical solution is visualized graphically by MATLAB to describe the dynamics of desired solution.

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