International Journal of Applied Nonlinear Science (7 papers in press)

Regular Issues

• Evolutionary artificial intelligence in the Industry 4.0 to simulate static loads in railway tracks for geosynthetic-reinforced soil structures based geogrid  
  by M.A. Balasubramani, R. Venkatakrishnaiah, K.V.B. Raju 
  Abstract: In order to evaluate the internal stabilities of geogrid-reinforced pile-supported foundation (GRPSF) constructions, a precise estimation of the reinforcing tensile stresses is essential. In this study, we use experimental research and finite element modelling to examine the effects of geogrid on the stability and settlement of elevated railway embankments. The first embankments were not geogrid-reinforced. An adaptive metaheuristic intelligence model was created to estimate reinforcement loads effectively and accurately. The proposed model improves the prediction ability of the artificial neural network (ANN) technology by adding the intelligent components of neurons. Using a range of acknowledged statistical markers, the models predictive power was assessed and confirmed against several independent scientific studies published in the literature. A sensitivity analysis was used to further test the models dependability and robustness. The suggested ANN model can intelligently and accurately estimate the maximum settling of GRPSF under service loads, making it a useful prediction tool for early GRPSF design. Engineers conducted computer simulations to place geogrid layers on the second through fifth embankments. The settlements of these berms were compared after being loaded with anywhere from one to four layers of geogrid.
  Keywords: geogrid-reinforced pile-supported foundation; GRPSF; settlement; testing; settlement; geosynthetic-reinforced soil; ballasted; Sslab track; predictive modelling; artificial intelligence in the Industry 4.0; artificial neural network; ANN.
  DOI: 10.1504/IJANS.2023.10059135
   
  
• A study of COVID-19 spread through zipper fractal interpolation  
  by Sneha, Kuldip Katiyar 
  Abstract: This note aims to study a reconstruction model of pandemic curves based on fractal interpolation function point of view. The weekly confirmed positive cases starting from October 1, 2021 to April 14, 2022 of the ten countries, the UK, India, South Africa, Brazil, France, Netherlands, Australia, Italy, Belgium, and Israel has been studied by using the fractal techniques. The fractal interpolation scheme used in this paper, called zipper fractal interpolation function (ZFIF) is based on concept of zipper functions. The embedding of zipper function in fractal interpolation provides more flexibility and versatility to analyse the pandemic curves. The ZFIFs are then tested for a case study of above-mentioned countries and obtain many interesting results.
  Keywords: COVID-19; pandemic curve; zipper; fractal interpolation function; FIF; zipper FIF.
  DOI: 10.1504/IJANS.2022.10054640
   
  
• Generalisation of Ostrowski's type inequalities by using multi-step quadratic kernel  
  by Tasawar Abbas, Muhammad Mohsin Saleem Kamboh, Muhammad Sultan, Hafiz Muhammad Waseem Anwar, Ather Qayyum 
  Abstract: The purpose of this paper is to provide a better version of Ostrowski's type integral inequalities. The inequalities are obtained by using a newly developed special type of nine-step quadratic kernel. The introduction of this new kernel gives some new error bounds for various quadrature rules. Applications for composite quadrature rules are also considered.
  Keywords: Ostrowski inequality; numerical integration; composite quadrature rule; cumulative distributive function.
  DOI: 10.1504/IJANS.2023.10054502
   
  
• Soliton solutions of space-time fractional Zoomeron differential equation  
  by Hamood Ur Rehman, Muhammad Imran Asjad, Ifrah Iqbal, Ali Akgül 
  Abstract: In the present work, Sardar subequation method (SSM) is exerted for seeking exact solutions of (2 + 1)-dimensional space-time fractional Zoomeron equation (FZE) in terms of conformable derivative (CD). The conformable derivative has much more capability than Riemann-Liouville and caputo derivative in solving the nonlinear fractional differential equation. The proposed method is extremely simple and very effective for finding exact solutions and then extracting solitons for the model. Bright, dark, singular, periodic singular and bright-dark hybrid soliton solutions are retrieved. Appropriate constraints are chosen for the obtained solitons to guarantee their existence. Moreover, from some obtained solutions, we draw its two-dimensional, contour and three-dimensional graphs by taking suitable values of parameters and then compare these graphs by changing the values of conformable derivative.
  Keywords: space-time fractional Zoomeron equation; FZE; Sardar subequation method; SSM; conformable derivative; CD; nonlinear partial fractional differential equations; NLFPDEs.
  DOI: 10.1504/IJANS.2023.10059378
   
  
• Some results on generalised Euler-type integrals related to the k-Wright function  
  by Muhammad Asif, Adnan Khan, Ali Akgül, Biniyam Shimelis 
  Abstract: Special functions such that Zeta, Bessel, Whittaker, Struve, Airy, Weber-Hermite and k-Wright functions are obtained as a solution to complex differential equations in engineering. In this work, generalised Euler-type integrals involving k-Wright function are suggested. Some special cases of this type of generalised integrals that are corresponding to well-known results in the literature are also inferred. We also study extended beta and associated functions (Gauss hypergeometric and confluent hypergeometric functions) connected to k-Wright function. For the newly extended beta, Gauss hypergeometric and confluent hypergeometric functions.
  Keywords: Beta functions; Euler-type function; Gamma function; k-Wright function.
  DOI: 10.1504/IJANS.2023.10056451
   
  
• Design of an optimal step-by-step sliding mode observer for multiple fractional-order chaotic synchronisation with an application to secure communication  
  by Mahedi Abdelghani Atoussi, Slami Saadi, Bachir Nail 
  Abstract: The aim of this study is to achieve the best synchronisation in a secure communication scheme by using two fractional-order chaotic systems (FOCS), one for the transmitter and the other for the receiver. This synchronisation is done with the assistance of the step-by-step sliding mode observer (SBS-SMO). To improve the observer's performance, a novel optimisation algorithm called the artificial hummingbird algorithm (AHA) had been used, which leads to selecting the best parameters for the observer instead of selecting them randomly. The proposed scheme succeeded in recovering the secret message that could be (signal, voice, etc.) in the receiver section in a finite period of time.
  Keywords: fractional-order systems; secure communication; Chua's systems; synchronisation; chaotic systems; artificial hummingbird algorithm; AHA.
  DOI: 10.1504/IJANS.2023.10056188
   
  
• Adaptive recursive least squares method for parameter estimation of autoregressive models  
  by Shazia Javed, Ghida Nazir, Nazir Ahmad Chaudhry, Ali Akgül, Muhammad Farhan Tabassum 
  Abstract: The recursive least squares (RLS) methods are extremely used to find the solutions of problems in many areas, such as communication, signal processing, optimisation and control. In this paper the RLS algorithm is modified for parameter estimation of regression models, such as the pseudo-linear ARMA (PS-ARMA) model and output error autoregressive (OEAR) model. The adaptive filtering technique with random input-output is used in the proposed recursive parameter estimation (RPE) algorithm to recursively predict the exact set of parameters for any regression model. The proposed method works by predicting an output signal that is adaptively improved to approximate the desired filter output. The experimental results are provided to prove the effectiveness of the proposed method.
  Keywords: adaptive filter; autoregressive model; parameter estimation; random signals.
  DOI: 10.1504/IJANS.2023.10057455