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This paper presents the study of fractional Emden–Fowler (FEF) equations by utilizinga new adequate procedure, specifically the q- homotopy analysis transform method (q- HATM). The EF equation has got greater significance in both physical and mathematical investigation of capillary and nonlinear dispersive gravity waves. The projected technique is tested by considering four illustrations of the time-fractional EF equations. The q -HATM furnish ℏ , known as an auxiliary parameter, by the support of ℏ we can modulate the various stages of convergence of the series solution. Additionally, to certify the resolution and accurateness of the proposed method we fitted the suitable numerical simulations. The redeem results guarantee that the proposed process is more convincing and scrutinizes the extremely nonlinear issues emerging in the field of science and engineering. • q -HATM is applied to obtain the solution to fractional Emden-Fowler equations. • Accuracy of the proposed method is validated through suitable numerical simulations. • The proposed method is efficient to study nonlinear issues in the areas of science. [ABSTRACT FROM AUTHOR]

In the present work, the numerical solutions for time-fractional coupled Burgers equations are obtained with the aid of q -homotopy analysis transform method (q -HATM). The study of coupled Burgers equations plays a vital role in a model of evolution of the scaled volume concentration or sedimentation of the two kind particles in fluid suspensions of colloids, under the effect of gravity. In this paper, the fractional derivative is considered in Caputo sense and the proposed algorithm is an elegant mixture of homotopy analysis technique with Laplace transform. The convergence analysis for the proposed algorithm is demonstrated. The obtained solutions are presented in a series form, which converges swiftly. In order to verify the proposed technique is reliable and accurate, the numerical simulations have been conducted. The results of the study divulge that, the future technique is computationally very effective and more accurate to analyse fractional nonlinear coupled Burgers differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a three-dimensional Lotka–Volterra attractor in the frame of the Caputo fractional derivative to examine its dynamics. The theoretical concepts like existence and uniqueness and boundedness of the solution are analyzed. To regulate the chaos in this fractional-order system, we have developed a sliding mode controller and conditions for global stability of the controlled system with and without uncertainties and outside disruptions are derived. The ability of the designed controller is examined in terms of both commensurate and non-commensurate fractional order derivatives for all the aspects. The Lyapunov exponent is the novelty of this paper which is used to illustrate the behavior of the chaos and demonstrate the dissipativeness of the considered chaotic system. We have examined the effect of fractional order derivatives in this system. With the help of numerical simulations, the theoretical claims regarding the impact of the controller on the system are established. [ABSTRACT FROM AUTHOR]

The goal of this work is to investigate nonlinear models and their complexity using techniques that are universal and have connections to historical and material aspects. Using the premise of a constant population that is uniformly mixed, a nonlinear compartmental model that depicts the movement between voter classes is taken into consideration. In the current work, we investigate the dynamical framework that supports the interactions between the three parties. It is discussed how rate change affects various metrics. The conditions for boundedness, stability, existence, and other dynamics are obtained. We derive the effects of generalizing the model in any order. The current study supports investigations into complex real-world issues and forecasts of necessary plans. [ABSTRACT FROM AUTHOR]