Numerical solutions of time-fractional Klein-Gordon equations by clique polynomials

Ganji, R.M.; Jafari, Hossein; Kgarose, Maluti; Mohammadi, Ardeshir Karami

doi:10.1016/j.aej.2021.03.026

Cited by 71 publications

(14 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For α � 1, the series expansions (66) have the forms, y 1 (t) � e − 2t , y 2 (t) � e − t which are coincide with the exact solutions for the ordinary system ( 47) and (48).…”

Section: Numerical Examplesmentioning

confidence: 71%

See 1 more Smart Citation

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Qazza

Burqan

Saadeh

2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this research, systems of linear and nonlinear differential equations of fractional order are solved analytically using the novel interesting method: ARA- Residual Power Series (ARA-RPS) technique. This approach technique is based on the combination of the residual power series scheme with the ARA transform to establish analytical approximate solutions in a fast convergent series representation using the concept of the limit. The proposed method needs less time and effort compared with the residual power series technique. To prove the simplicity, applicability, and reliability of the presented method, three numerical examples are proposed and simulated. The obtained results show that the ARA-RPS technique is applicable, simple, and effective to get solutions to linear and nonlinear engineering and physical problems.

show abstract

“…For α � 1, the series expansions (66) have the forms, y 1 (t) � e − 2t , y 2 (t) � e − t which are coincide with the exact solutions for the ordinary system ( 47) and (48).…”

Section: Numerical Examplesmentioning

confidence: 71%

“…We mention that our results are obtained by using the Mathematica software package 12. As future work, we plan to solve fractional integral equations and systems of fractional partial differential equations with different orders of α using the proposed method [48][49][50].…”

Section: Discussionmentioning

confidence: 99%

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Qazza

Burqan

Saadeh

2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…This model was an extension of a simple two-dimensional mathematical model of glioma growth and diffusion. In [ 3 ] the Klein-Gordon equation (KGE) which has many scientific applications such as quantum field theory, nonlinear optics and solid state physics is investigated. Jafari et al [ 4 ], examined the population dynamics model, including the hunting-hunting problem where the logistics equation, is generalized using the fractional operator.…”

Section: Introduction and Basic Definitionsmentioning

confidence: 99%

Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

Pourdarvish

Sayevand

Masti

et al. 2022

Int. J. Appl. Comput. Math

View full text Add to dashboard Cite

Analyzing the mathematical models involving Itô integral, in particular in science and engineering has received much attention, and the reason for this issue is the randomness and lack of access to the exact answer of this type of models. For this purpose, in this paper, the approximate solution of two dimensional (2-D) stochastic Volterra–Fredholm integral equations (SVFIEs) based on the operational matrix method and orthonormal Bernoulli polynomials (OBP) is investigated. Some results and convergence analysis are also presented. Finally, by presenting three examples and reviewing the results and numerical comparisons, we showed that the proposed method has an excellent performance.

show abstract

“…Various technical aspects involving the formation, detection, and simulation of heat within living tissues have been extensively researched. [8][9][10][11][12][13][14] To assess the temperature distribution within biological tissues, a trustworthy thermal approach that can properly interpret temperature equations is necessary. Fahmy 15 studied at how to solve the biothermal two-dimensional (2D) delayed phase bioheat transfer equation using a new boundary element method.…”

Section: Introductionmentioning

confidence: 99%

“…Hyperthermia is a therapy employed by oncologists to cure malignant and benign tumors by applying heat in a variety of ways. Various technical aspects involving the formation, detection, and simulation of heat within living tissues have been extensively researched 8–14 . To assess the temperature distribution within biological tissues, a trustworthy thermal approach that can properly interpret temperature equations is necessary.…”

Section: Introductionmentioning

confidence: 99%

Analytical assessment of the time‐space fractional bioheat transfer equation by the radial basis function method for living tissues

et al. 2022

View full text Add to dashboard Cite

In recent years, thermal treatment has proven to be helpful, notably in oncology. In fact, ablating the superfluous mass and eliminating the malignant tumor using a different modality such as warmth or cooling is a therapeutic method. In this study, the radial basis function approach was used to answer the time-space fractional heat transfer equations of human body tissue during thermal therapy. To validate the radial basis function technique, it was also compared to the fourthorder Runge-Kutta numerical method. The findings demonstrated that this methodology is extremely accurate and efficient, with an error rate of less than 1%. The effect of time and spatial fractional parameters, blood perfusion coefficient, metabolic coefficient, and internal source coefficient on the temperature profile inside human living tissues has been studied and depicted well.

show abstract

Numerical solutions of time-fractional Klein-Gordon equations by clique polynomials

Cited by 71 publications

References 29 publications

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

Analytical assessment of the time‐space fractional bioheat transfer equation by the radial basis function method for living tissues

Contact Info

Product

Resources

About