In this study, we examine the Kuramoto-Sivashinsky equation, which is a nonlinear model that describes several physical and chemical events arising in fluid flow. The approximate analytical solution for the fractional KS (FKS) problem is calculated using the Temimi-Ansari method (TAM) and the natural decomposition method (NDM). The projected procedure (NDM) combines the adomian decomposition method with the natural transform. Each technique can deal with nonlinear terms without making any assumptions. The methodologies under consideration provide english\omega _{n}-curves that display the convergence window of the power series solution that approaches the exact solution. We explore two distinct examples to confirm the efficiency and applicability of the proposed strategies. The acquired outcomes are compared numerically with the q-homotopy analysis transform method (q-HATM). The numerical investigation is carried out to validate the precision and dependability of the approaches under consideration. Additionally, the nature of the outcomes gained has been displayed in a different order. The obtained results show that the proposed techniques are highly efficient and simple to use to analyze the behavior of other nonlinear models.
Abstract In this study, we examine the Kuramoto-Sivashinsky equation, which is a nonlinear model that describes several physical and chemical events arising in fluid flow. The approximate [...]
In today’s world, analyzing nonlinear occurrences related to physical phenomena is a hot topic. The main goal of this research is to use the natural decomposition method (NDM) of fractional order to find an approximate solution to the fractional clannish random walker’s parabolic (CRWP) equation. The proposed method gives approximate solutions that are exceptionally near the exact solution without the complication that numerous other techniques imply. Banach’s fixed-point theory is used to investigate the anticipated issue’s convergence analysis and uniqueness theorem. To ensure that the suggested technique is trustworthy and precise, numerical simulations were conducted. The results are shown in the graphs and tables. When comparing the proposed scheme’s solution to the actual solutions, it becomes clear that the scheme is efficient, systematic, and very precise when dealing with nonlinear complex phenomena.
Abstract In today’s world, analyzing nonlinear occurrences related to physical phenomena is a hot topic. The main goal of this research is to use the natural decomposition method [...]
This article introduces and illustrates a novel approximation to the compound KdV-Burgers equation. For such a challenge, the q-homotopy analysis transform technique (q-HATM) is a potent approach. The suggested procedure avoids the complexity seen in many other methods and provides an approximation that is extremely near to the exact solution. The uniqueness theorem and convergence analysis of the expected problem are explored with the aid of Banach's fixed-point theory. Through a difference in the fractional derivative, the normal frequency for the fractional solution to this issue changes. All of the discovered solutions are illustrated in the figures and tables.
Abstract This article introduces and illustrates a novel approximation to the compound KdV-Burgers equation. For such a challenge, the q-homotopy analysis transform technique (q-HATM) [...]
The analysis of nonlinear events related to physical phenomena is a popular issue in the modern-day. The essential purpose of this work is to discover a novel approximate solution to the fractional nonlinear Benjamin Bona Mahony Peregrine Burgers equation (BBMPB) utilizing the natural decomposition method (NDM) of fractional order. The suggested approach provides analytical solutions that are extremely near to the exact solution whereas obviating the complexities associated with many other approaches. The expected issue’s uniqueness theorem and convergence analysis are explored using Banach’s fixed-point theory. The reliability and accuracy of the recommended method were tested using numerical simulations. The graphs and tables reflect the results. The comparison of the suggested scheme’s solution with the exact solutions demonstrates that the scheme is efficient, methodical, and extremely exact in tackling nonlinear complicated phenomena.
Abstract The analysis of nonlinear events related to physical phenomena is a popular issue in the modern-day. The essential purpose of this work is to discover a novel approximate [...]
Food security has become a significant issue due to the growing human population. In this case, a significant role is played by agriculture. The essential foods are obtained mainly from plants. Plant diseases can, however, decrease both food production and its quality. Therefore, it is substantial to comprehend the dynamics of plant diseases as they can provide insightful information about the dispersal of plant diseases. In order to investigate the dynamics of plant disease and analyze the effects of strategies of disease control, a mathematical model can be applied. We show that this model provides the non-negative solutions that population dynamics requires. The model was investigated by using the Atangana-Baleanu in Caputo sense (ABC) operator which is symmetrical to the Caputo-Fabrizio (CF) operator with a different function. Whereas the ABC operator uses the generalized Mittag-Leffler function while the CF operator employs the exponential kernel. For the proposed model, we have displayed the local and global stability of a nonendemic and an endemic equilibrium, existence and uniqueness theorems. By applying the fractional Adams-Bashforth-Moulton method, we have implemented numerical solutions to illustrate the theoretical analysis.
Abstract Food security has become a significant issue due to the growing human population. In this case, a significant role is played by agriculture. The essential foods are obtained [...]
Reliable iterative techniques for solving the KS equation arising in fluid flow 
