Numerical study of nonlinear 2D optimal control problems with multi-term variable-order fractional derivatives in the Atangana-Baleanu-Caputo sense

Pho, Kim-Hung; Heydari, Mohammad Hossein; Tuan, Bui Anh; Mahmoudi, Mohammad Reza

doi:10.1016/j.chaos.2020.109695

Cited by 17 publications

(11 citation statements)

References 26 publications

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“…These research tools have an important practical application, such as the study of the Covit-19 disease. About related research topics can look in Maleki et al 26,27 , Pho, K. H. 28 .…”

Section: Discussionmentioning

confidence: 99%

Risk Factors of Lung Cancer Patients: A Survival Analysis with R

Nguyen

2020

Sci. Tech. Dev. J.

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Introduction: This paper studies risk factors which can have effects on the survival time of lung cancer patients during the treatment. Methods: The Cox proportional-hazards model has been applied for investigating the association between the survival time of patients and the predictors such as age, gender, the weight of patients, meal, the ECOG, and Karnofsky scores. Results: In the study, we find that the ECOG score, the Karnofsky score evaluated by doctors and the gender are the top three factors that significantly affect the hazard rate. Also, we utilize the estimated model to predict survival probability for the patients. Conclusion: In this article, we intentionally present a complete and detailed guide on how to perform a R-based package in survival analysis step by step as well as how to interpret all output results.

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“…These research tools have an important practical application, such as the study of the Covit-19 disease. About related research topics can look in Maleki et al 26,27 , Pho, K. H. 28 .…”

Section: Discussionmentioning

confidence: 99%

Risk Factors of Lung Cancer Patients: A Survival Analysis with R

Nguyen

2020

Sci. Tech. Dev. J.

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“…The purpose of this paper is to express the function ψ j ðtÞ, j = 0, 1, 2, ⋯, n + 1, as an operational matrix as follows [39]:…”

Section: Approximation Function and Properties Of The Lagrange And The Ccf Polynomialsmentioning

confidence: 99%

New Numerical Algorithm to Solve Variable-Order Fractional Integrodifferential Equations in the Sense of Hilfer-Prabhakar Derivative

Derakhshan

2021

Abstract and Applied Analysis

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In this article, a numerical technique based on the Chebyshev cardinal functions (CCFs) and the Lagrange multiplier technique for the numerical approximation of the variable-order fractional integrodifferential equations are shown. The variable-order fractional derivative is considered in the sense of regularized Hilfer-Prabhakar and Hilfer-Prabhakar fractional derivatives. To solve the problem, first, we obtain the operational matrix of the regularized Hilfer-Prabhakar and Hilfer-Prabhakar fractional derivatives of CCFs. Then, this matrix and collocation method are used to reduce the solution of the nonlinear coupled variable-order fractional integrodifferential equations to a system of algebraic equations which is technically simpler for handling. Convergence and error analysis are examined. Finally, some examples are given to test the proposed numerical method to illustrate its accuracy and efficiency.

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“…The cardinality enables us to compute exactly the CCFs expansion coefficients of a function. Recently, these functions have been utilized to solve various equations, including a category of systems of VO fractional quadratic integral equations, 51 VO fractional optimal control problems, 52 VO fractional 2D Kuramoto–Sivashinsky equation, 53 VO fractional pantograph equation, 54 coupled fractal‐fractional Schrödinger equations, 55 and coupled VO fractional sine‐Gordon equations 7 …”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of variable‐order fractional Benjamin–Bona–Mahony–Burgers equation using a pseudo‐spectral method

Heydari

Razzaghi

Avazzadeh

2021

Math Methods in App Sciences

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This article introduces a new local variable‐order (VO) fractional differentiation called the VO conformable fractional derivative. This derivative is employed to define the VO time fractional Benjamin–Bona–Mahony–Burgers (BBMB) equation. A pseudo‐spectral algorithm using the Chebyshev cardinal functions (CCFs) is adopted to find a numerical solution for this equation. The presented method with the help of the CCFs derivative matrices (which are obtained in this research) turns problem solving into solving an algebraic system of equations. The proposed approach is applied on some test problems, and its accuracy is examined in terms of L∞ and L2 error norms. A numerical comparison is performed between the achieved results of the method with the results obtained from the cubic B‐spline method and the hybrid method generated using the quintic Hermite approach and the finite difference technique.

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Numerical study of nonlinear 2D optimal control problems with multi-term variable-order fractional derivatives in the Atangana-Baleanu-Caputo sense

Cited by 17 publications

References 26 publications

Risk Factors of Lung Cancer Patients: A Survival Analysis with R

Risk Factors of Lung Cancer Patients: A Survival Analysis with R

New Numerical Algorithm to Solve Variable-Order Fractional Integrodifferential Equations in the Sense of Hilfer-Prabhakar Derivative

Numerical investigation of variable‐order fractional Benjamin–Bona–Mahony–Burgers equation using a pseudo‐spectral method

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