A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

We propose a new modification of homotopy perturbation method (HPM) called the δ-homotopy perturbation transform method (δ-HPTM). This modification consists of the Laplace transform method, HPM, and a control parameter δ. This control convergence parameter δ in this new modification helps in adjusting and controlling the convergence region of the series solution and overcome some limitations of HPM and HPTM. The δ-HPTM and q-homotopy analysis transform method (q-HATM) are considered to study the generalized time-fractional perturbed $(3+1)$ ( 3 + 1 ) -dimensional Zakharov–Kuznetsov equation with Caputo fractional time derivative. This equation describes nonlinear dust-ion-acoustic waves in the magnetized two-ion-temperature dusty plasmas. The selection of an appropriate value of δ in δ-HPTM and the auxiliary parameters n and ħ in q-HATM gives a guaranteed convergence of series solution, but the difference between the two techniques is that the embedding parameter p in δ-HPTM varies from zero to nonzero δ, whereas the embedding parameter q in q-HATM varies from zero to $\frac{1}{n}, n\geq{1}$ 1 n , n ≥ 1 . We examine the effect of fractional order on the considered problem and present the error estimate when compared with exact solution. The outcomes reveal complete reliability and efficiency of the proposed algorithm for solving various types of physical models arising in sciences and engineering. Furthermore, we present the convergence and error analysis of the two methods.

show abstract

“…To exemplify the idea of q-HATM [68][69][70][71][72][73][74][75], we construct the zeroth-order deformation equation for 0…”

Section: The Q-homotopy Analysis Transform Methods (Q-hatm)mentioning

confidence: 99%

Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…It should be noted here that solving fractional dierential equations is very dicult due to the memory eect. Beyond numerical methods, which often time are computationally demanding, dierent analytical methods have been proposed to handle linear and nonlinear fractional dierential equations, see [23,24,25,26,27,28,13,29,30].…”

Section: Introductionmentioning

confidence: 99%

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Iyiola¹,

Oduro²,

Zabilowicz³

et al. 2021

Preprint

View full text Add to dashboard Cite

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalization and deaths have been observed, and thousands of cases daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to understand the transmission of the disease better. Nonlocality involved in the model has made fractional differential equations appropriate for modeling the behavior. However, solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate (from exposed quarantine and recovered to susceptible and infected quarantined individuals), quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium analysis, and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam-Bashforth-Moulton method developed for the fractional order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19, especially quarantining exposed and infected individuals and the effective contact rate. Based on the results with different fractional order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is what is happening right now in many countries.

show abstract

“…Fractional calculus, which is a generalization of differentiation and integration of integer order, has been proposed to overcome many of the restrictions associated with integer order derivatives. Beyond biological systems, noninteger order derivatives have been successfully used to model physical phenomena in medicine, physics, image processing, optimization, electrodynamics, nanotechnology, biotechnology, engineering in general, and many more, see [10][11][12][13][14][15][16][17][18][19] [20][21][22], Laplace analysis method [23], homotopy analysis method [24][25][26][27][28], Adomian decomposition method [29], differential transformation method [30], perturbation-iteration algorithm [31], iterative Shehu transform method [32], residual power series method [33][34][35][36][37][38][39][40][41], and q-homotopy analysis transform method in [42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

A fractional order approach to modeling and simulations of the novel COVID-19

et al. 2020

Self Cite

View full text Add to dashboard Cite

The novel coronavirus (SARS-CoV-2), or COVID-19, has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public health challenges in modern times, with no proven cure or vaccine. In this paper, our focus is on a fractional order approach to modeling and simulations of the novel COVID-19. We introduce a fractional type susceptible–exposed–infected–recovered (SEIR) model to gain insight into the ongoing pandemic. Our proposed model incorporates transmission rate, testing rates, and transition rate (from asymptomatic to symptomatic population groups) for a holistic study of the coronavirus disease. The impacts of these parameters on the dynamics of the solution profiles for the disease are simulated and discussed in detail. Furthermore, across all the different parameters, the effects of the fractional order derivative are also simulated and discussed in detail. Various simulations carried out enable us gain deep insights into the dynamics of the spread of COVID-19. The simulation results confirm that fractional calculus is an appropriate tool in modeling the spread of a complex infectious disease such as the novel COVID-19. In the absence of vaccine and treatment, our analysis strongly supports the significance reduction in the transmission rate as a valuable strategy to curb the spread of the virus. Our results suggest that tracing and moving testing up has an important benefit. It reduces the number of infected individuals in the general public and thereby reduces the spread of the pandemic. Once the infected individuals are identified and isolated, the interaction between susceptible and infected individuals diminishes and transmission reduces. Furthermore, aggressive testing is also highly recommended.

show abstract

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

Cited by 45 publications

References 58 publications

Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

A fractional order approach to modeling and simulations of the novel COVID-19

Contact Info

Product

Resources

About