Advances in solving conformable nonlinear partial differential equations and new exact wave solutions for Oskolkov‐type equations

Thabet, Hayman; Kendre, Subhash; Peters, James F.

doi:10.1002/mma.7945

Cited by 10 publications

(19 citation statements)

References 39 publications

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“…The graphs for the susceptible population s 1 (x, t) in system (33) for 𝛼 = 0.5 (on the left) and 𝛼 = 1 (on the right). It is expected to have more cases in the susceptible population when the time increases during the pandemic.…”

Section: Figurementioning

confidence: 99%

“…The graphs for the infected population i 1 (x, t) in system (33) for 𝛼 = 0.5 (on the left) and 𝛼 = 1 (on the right). We see that number of cases slowly increases during the pandemic time.…”

Section: Figurementioning

confidence: 99%

“…One of the most powerful methods for obtaining an exact solution is the exponential rational function method (ERFM). The ERFM has been widely used to obtain a series of exact solutions for higher dimensional nonlinear PDEs; see, for example, Ghanbari et al [29] introduced exact solutions of Biswas-Milovic equation by an ERFM, Ghanbari et al [30] introduced a generalized ERFM for extended Zakharov-Kuzetsov equation with conformable derivative, Kumar et al [31] obtained exact solitary wave solutions of the strain wave equation in microstructured solids via the generalized ERFM, Mohyud-Din and Bibi [32] obtained exact solutions for nonlinear fractional differential equations using the ERFM, and Thabet et al [33] introduced advances of ERFM and exact solutions of conformable PDEs.…”

Section: Introductionmentioning

confidence: 99%

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Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

Thabet

Kendre

2023

Math Methods in App Sciences

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Many challenges are still faced in bridging the gap between mathematical modeling and biological sciences. Measuring population immunity to assess the epidemiology of health and disease is a challenging task and is currently an active area of research. However, to meet these challenges, mathematical modeling is an effective technique in shaping the population dynamics that can help disease control. In this paper, we introduce a susceptible–infected–recovered (SIR) model and a susceptible–exposed–infected–recovered–deceased (SEIRD) model based on conformable space‐time partial differential equations (PDEs) for the coronavirus disease 2019 (COVID‐19) pandemic. As efficient analytical tools, we present new modifications based on the fractional exponential rational function method (ERFM) and an analytical technique based on the Adomian decomposition method for obtaining the solutions for the proposed models. These analytical approaches are more efficacious for obtaining analytical solutions for nonlinear systems of PDEs with conformable derivatives. The interesting result of this paper is that it yields new exact and approximate solutions to the proposed COVID‐19 pandemic models with conformable space‐time partial derivatives.

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Section: Figurementioning

confidence: 99%

Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

Thabet

Kendre

2023

Math Methods in App Sciences

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“…Fractional PDEs which involve fractional partial derivatives, in time or/and space, have been considered in many ways as a novel topic and they have been the subjects of several conferences due to their important applications in natural and applied sciences. [1][2][3][4][5][6][7][8][9][10][11]. Several problems in biology, ecology, ontology, and epidemiology need to be modeled in terms of fractional PDEs through mathematical modeling.…”

Section: Introductionmentioning

confidence: 99%

Fractional mathematical modeling for the transmission dynamics of SARS-CoV-2 infection

Thabet

Kendre

2023

Preprint

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This paper presents a mathematical model based on nonlinear PDEs of fractional veritable-order derivatives which describe the host population surviving on the transmission and evolution of the describes severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. Five host population groups have been considered, the susceptible, exposed, infected, recovered, and deceased (SEIRD) populations. The proposed model is governed by PDEs with fractional variable-order derivatives. The proposed model is new and has not been introduced before in its current formulation, therefore, the proposed technique is not compared with other techniques or real scenarios for the same model. The advantage of the used fractional partial derivatives of variable order that it can model the rate of change of subpopulation for the debated model. As an efficient tool to obtain the solution of the proposed model, a modified analytical technique based on the Adomian decomposition method is introduced. However, the present study is in general and can be applied to a host population of any country that can help inform public health interventions.

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“…The Oskolkov equation appears in various studies such as different types of traveling wave solutions of the Oskolkov equation have been investigated using the modified ( / ) GG  -expansion method [1], Ghanbari has been presented exact solutions for two Oskolkov-type equations [22], exact solutions have been attained for the Oskolkov equation [23], Thabet et al have been presented exact solutions for Oskolkov equations with exponential rational function method [24], Gozukızıl and Akcagıl have been created the exact solutions for the Oskolkov equation via tanh-coth method [25].…”

Section: Introductionmentioning

confidence: 99%

Sıkıştırılamaz Visko Elastik Kelvin-Voigt Sıvısında Ortaya Çıkan Oskolkov Denkleminin Gezici Dalga Çözümleri

Durur

2022

Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi

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In this manuscript, exact solutions of the Oskolkov equation, which describes the dynamics of incompressible viscoelastic Kelvin-Voigt fluid, are presented. The -expansion method is used to search for these solutions. The dynamics of the obtained exact solutions are analyzed with the help of appropriate parameters and presented with graphics. The applied method is efficient and reliable to search for fundamental nonlinear waves that enrich the various dynamical models seen in engineering fields. It is concluded that the analytical method used in the study of the Oskolkov equation is reliable, valid and useful tool for created traveling wave solutions.

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Advances in solving conformable nonlinear partial differential equations and new exact wave solutions for Oskolkov‐type equations

Cited by 10 publications

References 39 publications

Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

Fractional mathematical modeling for the transmission dynamics of SARS-CoV-2 infection

Sıkıştırılamaz Visko Elastik Kelvin-Voigt Sıvısında Ortaya Çıkan Oskolkov Denkleminin Gezici Dalga Çözümleri

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