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This article presents the novel fractional-order Genesio–Tesi system, along with discussions of its boundedness, stability of the equilibrium points, Lyapunov stability, uniqueness of the solution and bifurcation. The efficient predictor–corrector approach is employed to quantitatively analyse the Genesio–Tesi system in fractional order. The findings enable conceptualisation and visualisation of the presented novel fractional-order Genesio–Tesi systems. The modified systems are proposed for future study on chaos control and applying the same for secure communication. Bifurcation analysis is carried out to see the variation in the system's behaviour from stability to chaos. The results of the bifurcation analysis support the results obtained for the stability of the equilibrium points. The system behaves chaotically since all the equilibrium points are unstable. The findings demonstrate a torus attractor for some of the suggested systems and a chaotic attractor for some of the novel fractional-order Genesio–Tesi systems. The system's torus attractor changes into a steady state when the order is reduced from integer to fractional. Changing the parameter values for one of the modified systems also shifts the system's behaviour, with the point attractor replacing the torus attractor. The point attractor of one of the systems changes into a steady character when the system's order is reduced from integer to fractional. The behaviour for one modified system is the same for fractional and integer orders. This discovery paves the way for the future study of the modified Genesio–Tesi system. This article gives a new direction to utilise these proposed Genesio–Tesi systems and study them extensively. The chaotic behaviour of the modified system can be used for secure communication. The synchronisation and chaos control of the modified system is recommended. [ABSTRACT FROM AUTHOR]

In this article, we introduce analytical-approximate solutions of time-fractional generalized Pochhammer-Chree equations for wave propagation of elastic rod by means of the q-homotopy analysis of the transform method (q-HATM). In the Caputo sense, basic concepts for fractional derivatives are defined. Several examples are given and the results are illustrated via some surface plots to present the physical representation. The results show that the current methodology is productive, powerful, efficient, easy to use, and ready to incorporate a wide variety of partial fractional differential equations. [ABSTRACT FROM AUTHOR]

A new solution for fractional extended Fisher–Kolmogorov (FEFK) equation using the q-homotopy analysis transform method (q-HATM) is obtained. The fractional derivative considered in the present work is developed with Atangana–Baleanu (AB) operator, and the technique we consider is a mixture of the q-homotopy analysis scheme and the Laplace transform. The fixed point hypothesis is considered for the existence and uniqueness of the obtained solution of this model. For the validation and effectiveness of the projected scheme, we analyse the FEFK equation in terms of arbitrary order for the two distinct cases. Moreover, numerical simulation is demonstrated, and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured. [ABSTRACT FROM AUTHOR]

In this paper we study a special type of metric called ∗ -Ricci soliton on para-Sasakian manifold. We prove that if the para-Sasakian metric is a ∗ -Ricci soliton on a manifold M, then M is either D -homothetic to an Einstein manifold, or the Ricci tensor of M with respect to the canonical paracontact connection vanishes. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present work is to obtain an approximated analytical solution for the fractional smoking epidemic model with the aid of a novel technique called q-homotopy analysis transform method (q-HATM). The considered nonlinear mathematical model has been effectively employed to elucidate the evolution of smoking in a population and its impact on public health in a community. We find some new approximate solutions in a series form, which converges rapidly, and the proposed algorithm provides auxiliary parameters, which are very reliable and feasible in controlling the convergence of obtained approximate solutions. Further, we present novel simulations for all cases of results to validate the applicability and effectiveness of proposed scheme. The outcomes of the study reveal that the q-HATM is computationally very effective to analyse nonlinear fractional differential equations arises in daily life problems. [ABSTRACT FROM AUTHOR]

In the present work, an efficient numerical technique, called q-homotopy analysis transform method (briefly, q -HATM), is applied to nonlinear Fisher's equation of fractional order. The homotopy polynomials are employed, in order to handle the nonlinear terms. Numerical examples are illustrated to examine the efficiency of the proposed technique. The suggested algorithm provides the auxiliary parameters ħ and n , which help us to control and adjust the convergence region of the series solution. The outcomes of the study reveal that the q -HATM is computationally very effective and accurate to analyse nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

In the present investigation, the q-homotopy analysis transform method (q-HATM) is applied to find approximated analytical solution for the system of fractional differential equations describing the unsteady flow of a polytropic gas. Numerical simulation has been conducted to prove that the proposed technique is reliable and accurate, and the outcomes are revealed using plots and tables. The comparison between the obtained solutions and the exact solutions shows that the proposed method is efficient and effective in solving nonlinear complex problems. Moreover, the proposed algorithm controls and manipulates the obtained series solution in a huge acceptable region in an extreme manner and it provides us a simple procedure to control and adjust the convergence region of the series solution. [ABSTRACT FROM AUTHOR]

In this paper, a solution of coupled fractional Navier–Stokes equation is computed numerically using the proposed q-homotopy analysis transform method (q-HATM), and the solution is found in fast convergent series. The given test examples illustrate the leverage and effectiveness of the proposed technique. The obtained results are demonstrated graphically. The present method handles the series solution in a large admissible domain in an extreme manner. It offers us a modest way to adjust the convergence region of the solution. Results with graphs explicitly reveal the efficiency and capability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely the q-homotopy analysis transform method. These equations play a vital role in describing the properties of shallow water waves through distinct dispersion relation. The convergence analysis and error analysis are presented in the present investigation for the future scheme. We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to verify the accuracy. The numerical simulation is conducted to ensure the exactness of the future technique. The obtained numerical and graphical results are presented, the proposed scheme is computationally very accurate and straightforward to study and find the solution for fractional coupled nonlinear complex phenomena arising in science and technology. [ABSTRACT FROM AUTHOR]

Medicinal leaves are playing a vital role in our everyday life. There are an enormous amount of species present in the world. Identification of each type would be a tedious task. Using image processing technology, we can overcome this problem by providing computer vision with the help of a convolution neural network (CNN). The objective of this research is to find out the best CNN model that helps in classifying the plant leaf species and identifying its category. In this research work, the proposed basic CNN model consisting of four convolution layers uses ten different medicinal leaf species each belonging to two categories providing an accuracy of 96.88%\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$96.88\%$$\end{document}. [ABSTRACT FROM AUTHOR]