On the Wave Properties of the Conformable Generalized Bogoyavlensky–Konopelchenko Equation

Başkonuş, Hacı Mehmet; Senel, Mine; Kumar, Ajay; Yel, Gulnur; Şenel, Bilgin; Gao, Wei

doi:10.1201/9781003263517-5

Handbook of Fractional Calculus for Engineering and Science 2022

DOI: 10.1201/9781003263517-5

|View full text |Cite

On the Wave Properties of the Conformable Generalized Bogoyavlensky–Konopelchenko Equation

Hacı Mehmet Başkonuş¹,

Mine Senel²,

Ajay Kumar³

et al.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article3

Relationship

Self Cite1

Independent2

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In future work, this designed numerical BRNNA could be applied to solving various stiff nature models, including fractional love models [49,50], nonlinear fractional models [35], the Lonngren-wave equation [51], a Jeffrey fluid in contact with a Newtonian fluid [52], oscillation problems [53], quantum differential equations [54], the Bogoyavlensky-Konopelchenko model [55], and biological and fluid differential systems [35,[43][44][45][46][47][48][49][50][51][52][53][54][55].…”

mentioning

confidence: 99%

Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System

Sabir,

Hashem,

Arbi

et al. 2023

Mathematics

View full text Add to dashboard Cite

The present work provides the numerical solutions of the mathematical model based on the fractional-order Layla and Majnun model (MFLMM). A soft computing stochastic-based Bayesian regularization neural network approach (BRNNA) is provided to investigate the numerical accomplishments of the MFLMM. The nonlinear system is classified into two dynamics, whereas the correctness of the BRNNA is observed through the comparison of results. Furthermore, the reducible performance of the absolute error improves the exactitude of the computational BRNNA. Twenty neurons have been chosen, along with the data statics of training 74% and 13%, for both authorization and testing. The consistency of the designed BRNNA is demonstrated using the correlation/regression, error histograms, and transition of state values in order to solve the MFLMM.

show abstract

mentioning

confidence: 99%

Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System

Sabir,

Hashem,

Arbi

et al. 2023

Mathematics

View full text Add to dashboard Cite

show abstract

Dynamical behavior for the approximate solutions and different wave profiles nonlinear fractional generalised pochhammer-chree equation in mathematical physics

Kumar,

Fartyal

2023

Opt Quant Electron

Self Cite

View full text Add to dashboard Cite

In this Paper, fractional homotopy perturbation transform method (FHPTM) is used to obtain a variety of approximate solutions for the nonlinear fractional generalized Pochhammer-Chree equation which describes certain interesting higher-dimensional waves in harmonic studies, electrical, fluid mechanics, and other fields. By apply the caputo fabrizio derivative via laplace transform technique, we investigate all concerned wave models that have been used in the examination for the propagation of harmonic waves in a cylindrical rod and several problems in fluid mechanics and wave theory in physics. Banach's fixed point hypothesis is tested for governing fractional-order model in order to establish the existence and uniqueness of the achieved solution. We considered the model in terms of arbitrary order with three cases and introduced corresponding numerical simulations to demonstrate and validate the effectiveness of the proposed algorithm. By assigning appropriate values to free parameters, dynamical wave structures of some approximate solutions are graphically demonstrated using 2D and 3D fig. This method can also be used to approximate the solutions of other well-known equations in engineering physics, quantum field , and other applied sciences. Furthermore, various simulations are used to demonstrate the physical behaviors of the acquired solution with respect to fractional integer order.

show abstract

On dynamical behavior for approximate solutions sustained by nonlinear fractional damped Burger and Sharma–Tasso–Olver equation

Kumar¹,

Prasad²

2023

Int. J. Mod. Phys. B

View full text Add to dashboard Cite

In this paper, we study a nonlinear fractional Damped Burger and Sharma–Tasso–Olver equation using a new novel technique, called homotopy perturbation transform method (FHPTM). There are three examples used to demonstrate and validate the proposed algorithm’s efficiency. This nonlinear model depicts nonlinear wave processes in fluid dynamics, ecology, solid-state physics, shallow-water wave propagation, optical fibers, fluid mechanics, plasma physics, and other applied science, engineering, and mathematical physics disciplines, as well as other phenomena. Numerous algebraic properties of the fractional derivative Caputo–Fabrizio operator are illustrated concerning the Laplace transformation to demonstrate their utility. Different graphs and tables compare the results obtained by R. Nawaz et al. [Alex. Eng. J. 60, 3205 (2021)] and M. S. Rawashdeh [Appl. Math. Inform. Sci. 9, 1239 (2015)]. The proposed scheme accelerates the convergence of the series solution and guarantees the convergence associated with the homotopy parameter. Furthermore, the physical nature of various fractional orders has been captured in plots. The obtained results demonstrate that the employed solution procedure is dependable and methodical in investigating the behaviors of nonlinear models of both integer and fractional orders.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

On the Wave Properties of the Conformable Generalized Bogoyavlensky–Konopelchenko Equation

Cited by 3 publications

References 0 publications

Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System

Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System

Dynamical behavior for the approximate solutions and different wave profiles nonlinear fractional generalised pochhammer-chree equation in mathematical physics

On dynamical behavior for approximate solutions sustained by nonlinear fractional damped Burger and Sharma–Tasso–Olver equation

Contact Info

Product

Resources

About