He–elzaki Method for Spatial Diffusion of Biological Population

Rahman, Jamshaid Ul; Lu, Dianchen; Suleman, Muhammad; He, Ji‐Huan; Ramzan, Muhammad

doi:10.1142/s0218348x19500695

Cited by 35 publications

(15 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Annas et al constructed the mathematical model to study the influential behavior of coronavirus [ 4 , 5 ]; they also discussed the stability of their proposed model. Suleman et al, Ul Rahman et al, and Iqbal and Karaca numerically investigated the fractional model of HIV [ 6 , 7 , 8 ]. The National Health Organization instructed to keep away from infectious person or animals either with fever or any respiratory problems and also directed to wear surgical masks and directed continual use of hand sanitizers in public places for self-safety from infection.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Numerical Simulation for the Outbreak of COVID-19 Involving Loss of Immunity and Quarantined Class

Arif

Majeed

Rahman

et al. 2022

Computational and Mathematical Methods in Medicine

View full text Add to dashboard Cite

For the analysis of the recent deadly pandemic Sars-Cov-2, we constructed the mathematical model containing the whole population, partitioned into five different compartments, represented by SEIQR model. This current model especially contains the quarantined class and the factor of loss of immunity. Further, we discussed the stability of the SEIQR model (constructed on the basis of system of coupled differential equations). The basic reproduction that indicates the behavior of the disease is also estimated by the use of next-generation matrix method. Numerical simulation of this model is provided, the results are analyzed by theoretically strong numerical methods, and computationally known tool MATLAB Simulink is also used for visualization of the results. Validation of results by Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions on COVID-19. Our results suggest that the isolation of the active cases and strong immunization of patients or individuals play a major role to fight against the deadly Sars-Cov-2.

show abstract

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Numerical Simulation for the Outbreak of COVID-19 Involving Loss of Immunity and Quarantined Class

Arif

Majeed

Rahman

et al. 2022

Computational and Mathematical Methods in Medicine

View full text Add to dashboard Cite

show abstract

“…Laplace in 1780 [19,20] and Fourier in 1822. Recently, the idea of using integral transforms in solving differential equations and integral equations has been commonly used by many researchers in the literature [21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

A New Approach on Transforms: Formable Integral Transform and Its Applications

Saadeh

Ghazal

2021

Axioms

View full text Add to dashboard Cite

In this paper, we introduce a new integral transform called the Formable integral transform, which is a new efficient technique for solving ordinary and partial differential equations. We introduce the definition of the new transform and give the sufficient conditions for its existence. Some essential properties and examples are introduced to show the efficiency and applicability of the new transform, and we prove the duality between the new transform and other transforms such as the Laplace transform, Sumudu transform, Elzaki transform, ARA transform, Natural transform and Shehu transform. Finally, we use the Formable transform to solve some ordinary and partial differential equations by presenting five applications, and we evaluate the Formable transform for some functions and present them in a table. A comparison between the new transform and some well-known transforms is made and illustrated in a table.

show abstract

“…So far, many modified techniques have been described to solve linear and nonlinear differential equations of integer and fractional orders. Those of which are Laplace homotopy perturbation method, Laplace Adomian decomposition method, and recently, Elzaki homotopy transformation perturbation method is used to solve a range of problems such as a family of Fisher's equation [21], spatial diffusion of Biological population [22], nonlinear oscillators [23], system of linear and nonlinear PDEs of fractional orders [24], time-fractional Navier-Stokes equations [25], and An algorithm for solving the Burgers-Huxley equation using the Elzaki transform [26] Elzaki integral transform is a modification of the Laplace and Sumudu transforms which was invented by Tariq [27], Elzaki transformation is an efficient and powerful technique that has found the exact solutions to several differential equations which cannot be solved by Sumudu transform [28]. Elzaki integral equation is a powerful and efficient technique that has been used to solve many differential equations of integer and fractional orders [25][29]- [33].…”

Section: Introductionmentioning

confidence: 99%

A New Computational Method Based on Integral Transform for Solving Linear and Nonlinear Fractional Systems

et al. 2021

View full text Add to dashboard Cite

In this article, the Elzaki homotopy perturbation method is applied to solve fractional stiff systems. The Elzaki homotopy perturbation method (EHPM) is a combination of a modified Laplace integral transform called the Elzaki transform and the homotopy perturbation method. The proposed method is applied for some examples of linear and nonlinear fractional stiff systems. The results obtained by the current method were compared with the results obtained by the kernel Hilbert space KHSM method. The obtained result reveals that the Elzaki homotopy perturbation method is an effective and accurate technique to solve the systems of differential equations of fractional order.

show abstract

He–elzaki Method for Spatial Diffusion of Biological Population

Cited by 35 publications

References 46 publications

Mathematical Modeling and Numerical Simulation for the Outbreak of COVID-19 Involving Loss of Immunity and Quarantined Class

Mathematical Modeling and Numerical Simulation for the Outbreak of COVID-19 Involving Loss of Immunity and Quarantined Class

A New Approach on Transforms: Formable Integral Transform and Its Applications

A New Computational Method Based on Integral Transform for Solving Linear and Nonlinear Fractional Systems

Contact Info

Product

Resources

About