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

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.

Heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gladys Tharapatla ◽  
Pamula Rajakumari ◽  
Ramana G.V. Reddy
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Velocity Profile ◽  
Heat And Mass Transfer ◽  
Newtonian Fluids ◽  
Transfer Effects ◽  
Content Type ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Flow Through

Purpose This paper aims to analyze heat and mass transfer of magnetohydrodynamic (MHD) non-Newtonian fluids flow past an inclined thermally stratified porous plate using a numerical approach. Design/methodology/approach The flow equations are set up with the non-linear free convective term, thermal radiation, nanofluids and Soret–Dufour effects. Thus, the non-linear partial differential equations of the flow analysis were simplified by using similarity transformation to obtain non-linear coupled equations. The set of simplified equations are solved by using the spectral homotopy analysis method (SHAM) and the spectral relaxation method (SRM). SHAM uses the approach of Chebyshev pseudospectral alongside the homotopy analysis. The SRM uses the concept of Gauss-Seidel techniques to the linear system of equations. Findings Findings revealed that a large value of the non-linear convective parameters for both temperature and concentration increases the velocity profile. A large value of the Williamson term is detected to elevate the velocity plot, whereas the Casson parameter degenerates the velocity profile. The thermal radiation was found to elevate both velocity and temperature as its value increases. The imposed magnetic field was found to slow down the fluid velocity by originating the Lorentz force. Originality/value The novelty of this paper is to explore the heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium. The model is formulated in an inclined plate and embedded in a thermally-stratified porous medium which to the best of the knowledge has not been explored before in literature. Two elegance spectral numerical techniques have been used in solving the modeled equations. Both SRM and SHAM were found to be accurate.

scholarly journals Forecasting stock price movement: new evidence from a novel hybrid deep learning model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yang Zhao ◽  
Zhonglu Chen
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Hybrid Model ◽  
Stock Price ◽  
Linear Time ◽  
Price Movement ◽  
Content Type ◽  
Non Linear ◽  
New Evidence ◽  
Deep Learning Model

PurposeThis study explores whether a new machine learning method can more accurately predict the movement of stock prices.Design/methodology/approachThis study presents a novel hybrid deep learning model, Residual-CNN-Seq2Seq (RCSNet), to predict the trend of stock price movement. RCSNet integrates the autoregressive integrated moving average (ARIMA) model, convolutional neural network (CNN) and the sequence-to-sequence (Seq2Seq) long–short-term memory (LSTM) model.FindingsThe hybrid model is able to forecast both linear and non-linear time-series component of stock dataset. CNN and Seq2Seq LSTMs can be effectively combined for dynamic modeling of short- and long-term-dependent patterns in non-linear time series forecast. Experimental results show that the proposed model outperforms baseline models on S&P 500 index stock dataset from January 2000 to August 2016.Originality/valueThis study develops the RCSNet hybrid model to tackle the challenge by combining both linear and non-linear models. New evidence has been obtained in predicting the movement of stock market prices.

A novel approach for nonlinear equations occurs in ion acoustic waves in plasma with Mittag-Leffler law

2020 ◽  
Vol 37 (6) ◽  
pp. 1865-1897 ◽  
Author(s):  
P. Veeresha ◽  
D.G. Prakasha ◽  
Jagdev Singh
Keyword(s):  
Nonlinear Equations ◽  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Content Type ◽  
Physical Behaviour ◽  
Special Cases ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
The Future ◽  
Homotopy Analysis

Purpose The purpose of this paper is to find the solution for special cases of regular-long wave equations with fractional order using q-homotopy analysis transform method (q-HATM). Design/methodology/approach The proposed technique (q-HATM) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator. Findings The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional-order model. To illustrate and validate the efficiency of the future technique, the authors analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. Originality/value To illustrate and validate the efficiency of the future technique, we analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. The obtained results elucidate that, the proposed algorithm is easy to implement, highly methodical, as well as accurate and very effective to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

scholarly journals LPV robust servo control of aircraft active side-sticks

2020 ◽  
Vol 92 (4) ◽  
pp. 599-609
Author(s):  
Guang Rui Zhou ◽  
Shi Qian Liu ◽  
Yuan Jun Sang ◽  
Xu Dong Wang ◽  
Xiao Peng Jia ◽  
...  
Keyword(s):  
Control Method ◽  
Linear Time ◽  
External Disturbance ◽  
Servo System ◽  
Slip Angle ◽  
Content Type ◽  
Civil Aircraft ◽  
Non Linear ◽  
Lpv Control ◽  
The Impact

Purpose This paper aims to focus on the variable stick force-displacement (SFD) gradience in the active side stick (ASS) servo system for the civil aircraft. Design/methodology/approach The problem of variable SFD gradience was introduced first, followed by the analysis of its impact on the ASS servo system. To solve this problem, a linear-parameter-varying (LPV) control approach was suggested to process the variable gradience of the SFD. A H∞ robust control method was proposed to deal with the external disturbance. Findings To validate the algorithm performance, a linear time-variant system was calculated to be used to worst cases and the SFD gradience was set to linear and non-linear variation to test the algorithm, and some typical examples of pitch angle and side-slip angle tracking control for a large civil aircraft were also used to verify the algorithm. The results showed that the LPV control method had less settling time and less steady tracking errors than H∞ control, even in the variable SFD case. Practical implications This paper presented an ASS servo system using the LPV control method to solve the problem caused by the variable SFD gradience. The motor torque command was calculated by pressure and position feedback without additional hardware support. It was more useful for the electronic hydraulic servo actuator. Originality/value This was the research paper that analyzed the impact of the variable SFD gradience in the ASS servo system and presented an LPV control method to solve it. It was applicable for the SFD gradience changing in the linear and non-linear cases.

A numerical method for solving fractional differential equations

2019 ◽  
Vol 36 (2) ◽  
pp. 551-568
Author(s):  
Zain ul Abdeen ◽  
Mujeeb ur Rehman
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Fractional Differential Equations ◽  
Quadrature Rule ◽  
Benchmark Problems ◽  
Computational Technique ◽  
Algebraic Equations ◽  
Content Type ◽  
Non Linear ◽  
Fractional Differential

Purpose The purpose of this paper is to present a computational technique based on Newton–Cotes quadrature rule for solving fractional order differential equation. Design/methodology/approach The numerical method reduces initial value problem into a system of algebraic equations. The method presented here is also applicable to non-linear differential equations. To deal with non-linear equations, a recursive sequence of approximations is developed using quasi-linearization technique. Findings The method is tested on several benchmark problems from the literature. Comparison shows the supremacy of proposed method in terms of robust accuracy and swift convergence. Method can work on several similar types of problems. Originality/value It has been demonstrated that many physical systems are modelled more accurately by fractional differential equations rather than classical differential equations. Therefore, it is vital to propose some efficient numerical method. The computational technique presented in this paper is based on Newton–Cotes quadrature rule and quasi-linearization. The key feature of the method is that it works efficiently for non-linear problems.

scholarly journals REGARDING NEW NUMERICAL RESULTS FOR THE DYNAMICAL MODEL OF ROMANTIC RELATIONSHIPS WITH FRACTIONAL DERIVATIVE

Fractals ◽  
2021 ◽  
pp. 2240009
Author(s):  
WEI GAO ◽  
P. VEERESHA ◽  
D. G. PRAKASHA ◽  
HACI MEHMET BASKONUS
Keyword(s):  
Romantic Relationships ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Real Word ◽  
Transform Method ◽  
Coupled Equations ◽  
Fractional Order Differential Equations ◽  
Analysis Technique ◽  
Homotopy Analysis

The main purpose of the present investigation is to find the solution of fractional coupled equations describing the romantic relationships using [Formula: see text]-homotopy analysis transform method ([Formula: see text]-HATM). The considered scheme is a unification of [Formula: see text]-homotopy analysis technique with Laplace transform (LT). More preciously, we scrutinized the behavior of the obtained solution for the considered model with fractional-order, in order to elucidate the effectiveness of the proposed algorithm. Further, for the different fractional-order and parameters offered by the considered method, the physical natures have been apprehended. The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems.

scholarly journals Adaptive-Uniform-Experimental-Design-Based Fractional-Order Particle Swarm Optimizer with Non-Linear Time-Varying Evolution

2019 ◽  
Vol 9 (24) ◽  
pp. 5537 ◽  
Author(s):  
Po-Yuan Yang ◽  
Fu-I Chou ◽  
Jinn-Tsong Tsai ◽  
Jyh-Horng Chou
Keyword(s):  
Experimental Design ◽  
Fractional Order ◽  
Optimization Problems ◽  
Linear Time ◽  
Particle Swarm ◽  
Time Varying ◽  
Particle Swarm Optimizer ◽  
Local Optima ◽  
Non Linear ◽  
Velocity Derivative

An adaptive-uniform-experimental-design-based fractional particle swarm optimizer (AUFPSO) with non-linear time-varying evolution (NTE) is proposed. A particle swarm optimizer (PSO) is an excellent evolutionary algorithm due to its simple structure and rapid convergence. Nevertheless, PSO has notable drawbacks. Although many proposed methods and strategies have enhanced its effectiveness and performance, PSO is limited by its tendency to fall into local optima and its tendency to obtain different solutions in each search (i.e., its weak robustness). Introducing fractional-order calculus in PSO (FPSO) can correct the order of the velocity derivative for each particle, which enhances the diversity and algorithmic effectiveness. This study used NTE of the order of the velocity derivative, inertia weight, cognitive parameter, and social parameter in an FPSO used to search for a global optimal solution. To obtain the best combination of FPSO and NTE, an adaptive uniform experimental design (AUED) method was used to deal with this essential issue. The AUED method integrates a uniform layout with the best combination phase and a stepwise ratio to assist in selecting the best combination for FPSO-NTE. Experimental applications in 15 global numerical optimization problems confirmed that the AUFPSO-NTE had a better performance and robustness than existing PSO-related algorithms.

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