Novel approach for modified forms of Camassa–Holm and Degasperis–Procesi equations using fractional operator

Veeresha, P.; Prakasha, D. G.

doi:10.1088/1572-9494/aba24b

Cited by 18 publications

(6 citation statements)

References 41 publications

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“…Now, the nonlinear arbitrary-order differential equation is considered to demonstrate the algorithm [61][62][63][64][65][66][67][68][69] of the suggested algorithm…”

Section: Basic Procedures Of Projected Schemementioning

confidence: 99%

Numerical surfaces of fractional Zika virus model with diffusion effect of mosquito‐borne and sexually transmitted disease

Veeresha

Akinyemi

Oluwasegun

et al. 2021

Math Methods in App Sciences

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This paper analyzes the dynamics of fractional partial differential equation (FPDE) model of Zika virus that incorporates diffusion using Atangana-Baleanu (AB) fractional derivative. Zika virus disease is an infection transmitted predominantly by the bite of an infected Aedes species mosquito and may be a severe epidemic if not contained in its premature stages. The q-homotopy analysis transform method is employed to analyze and compute the solutions for this nonlinear partial differential model, and the fractional derivative is defined in Atangana-Baleanu sense. We determine some new approximate numerical results for different values of parameters of alpha. Numerical models focused on various distributions of the population help to explain how the spread of humans and mosquitoes influences the disease's transmission. With the utilization fixed-point hypothesis, the existence and uniqueness of the solutions obtained for the proposed model are presented.

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“…Now, the nonlinear arbitrary-order differential equation is considered to demonstrate the algorithm [61][62][63][64][65][66][67][68][69] of the suggested algorithm…”

Section: Basic Procedures Of Projected Schemementioning

confidence: 99%

Numerical surfaces of fractional Zika virus model with diffusion effect of mosquito‐borne and sexually transmitted disease

Veeresha

Akinyemi

Oluwasegun

et al. 2021

Math Methods in App Sciences

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“…The Lump and optical solitons solutions are derived by researchers in [35] with the analytical method, and authors in [36] derived some stimulating results associated with bipartite graph and fractional operator. The projected method is hired by the scholars to investigate the system associated with Jaulent-Miodek system with energy-dependent Schrödinger potential [37], the epidemic model of childhood disease [38], liquids with gas bubbles models [39], the Zakharov-Kuznetsov equation in dusty plasma [40], and Degasperis-Procesi equations [41]. In a two-dimensional channel flow, the impact of bottom configurations on the free-surface waves is investigated with the help of the forced Kortewegde Vries equation.…”

Section: Introductionmentioning

confidence: 99%

A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators

Veeresha

Yavuz

Baishya

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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The Korteweg–De Vries (KdV) equation has always provided a venue to study and generalizes diverse physical phenomena. The pivotal aim of the study is to analyze the behaviors of forced KdV equation describing the free surface critical flow over a hole by finding the solution with the help of q-homotopy analysis transform technique (q-HATT). he projected method is elegant amalgamations of q-homotopy analysis scheme and Laplace transform. Three fractional operators are hired in the present study to show their essence in generalizing the models associated with power-law distribution, kernel singular, non-local and non-singular. The fixed-point theorem employed to present the existence and uniqueness for the hired arbitrary-order model and convergence for the solution is derived with Banach space. The projected scheme springs the series solution rapidly towards convergence and it can guarantee the convergence associated with the homotopy parameter. Moreover, for diverse fractional order the physical nature have been captured in plots. The achieved consequences illuminates, the hired solution procedure is reliable and highly methodical in investigating the behaviours of the nonlinear models of both integer and fractional order.

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“…Diverse pioneering notions and fundamentals are prescribed by many senior researchers 1–6 . The FC turned out to be one of the most indispensable apparatuses to analyze and point out the nature of most complex and nonlinear phenomena 7–26 …”

Section: Introductionmentioning

confidence: 99%

Analysis of fractional‐order Schrödinger–Boussinesq and generalized Zakharov equations using efficient method

Benli

2021

Math Methods in App Sciences

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In this paper, we find the solution for an interesting family of coupled Schrödinger equations exemplifying simulating consequences. The fractional Schrödinger–Boussinesq (FSB) and fractional generalized Zakharov (FGZ) equations are analyzed in the present framework using fractional natural decomposition method (FNDM). The hired technique is graceful amalgamations of natural transform technique with Adomian decomposition scheme. Three different cases are considered, one with FSB equations and two cases are associated with FGZ equations with different initial conditions. To validate and illustrate the proficiency of the projected solution procedure, we analyzed the projected model in terms of fractional order. Further, we captured the nature of FNDM results for different values of fractional order in terms of the plots. The considered scheme is highly effective and structured while examining nonlinear models and which can be observed and confirmed from the obtained results. Moreover, the plots show that the hired fractional operator and algorithm can help to exemplify the more fascinating properties of the complex system associated with real‐world problems.

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Novel approach for modified forms of Camassa–Holm and Degasperis–Procesi equations using fractional operator

Cited by 18 publications

References 41 publications

Numerical surfaces of fractional Zika virus model with diffusion effect of mosquito‐borne and sexually transmitted disease

Numerical surfaces of fractional Zika virus model with diffusion effect of mosquito‐borne and sexually transmitted disease

A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators

Analysis of fractional‐order Schrödinger–Boussinesq and generalized Zakharov equations using efficient method

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