Conservatory of Kaup-Kupershmidt Equation to the Concept of Fractional Derivative with and without Singular Kernel

Atangana, Abdon; Goufo, Emile Franc Doungmo

doi:10.1007/s10255-018-0757-7

Cited by 11 publications

(3 citation statements)

References 16 publications

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“…Существует мнение, что модели дробного порядка более реалистичны, чем классические модели (см. [64,65,130,155,198,209,210]). В этой главе обсуждаются полулинейные дробные уравнения в банаховых пространствах, интенсивное изучение которых только начинается (см.…”

Section: полулинейные дробные уравненияunclassified

Аттракторы, Затенение И Аппроксимация Абстрактных Полулинейных Дифференциальных Уравнений

Piskarev¹,

Ovchinnikov²

2021

Итоги науки и техники. Серия «Современная математика и ее прило

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В обзоре обсуждаются такие разделы теории аппроксимации абстрактных дифференциальных уравнений как аппроксимация аттракторов в случае гиперболических стационарных точек, затенение и аппроксимация дробных по времени полулинейных задач.

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Section: полулинейные дробные уравненияunclassified

Аттракторы, Затенение И Аппроксимация Абстрактных Полулинейных Дифференциальных Уравнений

Piskarev¹,

Ovchinnikov²

2021

Итоги науки и техники. Серия «Современная математика и ее прило

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“…This article is dedicated to study the numerical solutions of fractional advection dispersion or diffusion equation with novel algorithm based on scale-3 Haar wavelets. There are various definitions of fractional derivatives are available in literature (Kilbas et al , 2006; Ahmad et al , 2019; Owolabi and Hammouch., 2019; Doungmo Goufo et al , 2018; Uçar et al , 2019; Asif et al , 2018; Doungmo Goufo, 2018; Atangana and Doungmo Goufo, 2018; Doungmo Goufo et al , 2020). Fractional space derivatives are used to model anomalous diffusion or dispersion, where a particle plume spreads at a rate inconsistent with the classical Brownian motion model, and the plume may be asymmetric.…”

Section: Introductionmentioning

confidence: 99%

A numerical algorithm based on scale-3 Haar wavelets for fractional advection dispersion equation

Pandit

Mittal

2020

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Purpose This paper aims to propose a novel approach based on uniform scale-3 Haar wavelets for unsteady state space fractional advection-dispersion partial differential equation which arises in complex network, fluid dynamics in porous media, biology, chemistry and biochemistry, electrode – electrolyte polarization, finance, system control, etc. Design/methodology/approach Scale-3 Haar wavelets are used to approximate the space and time variables. Scale-3 Haar wavelets converts the problems into linear system. After that Gauss elimination is used to find the wavelet coefficients. Findings A novel algorithm based on Haar wavelet for two-dimensional fractional partial differential equations is established. Error estimation has been derived by use of property of compactly supported orthonormality. The correctness and effectiveness of the theoretical arguments by numerical tests are confirmed. Originality/value Scale-3 Haar wavelets are used first time for these types of problems. Second, error analysis in new work in this direction.

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“…There are a number of different definitions of fractional-order derivatives, with different applications. An excellent overview can be found in the works [23][24][25][26][27][28][29][30][31]. This article is concerned with the following time-fractional non-linear Klein-Gordon equation (KGE):…”

Section: Introductionmentioning

confidence: 99%

Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

et al. 2020

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In this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein-Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order α ∈ (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme is O(h 2 + t 2−α) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.

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Conservatory of Kaup-Kupershmidt Equation to the Concept of Fractional Derivative with and without Singular Kernel

Cited by 11 publications

References 16 publications

Аттракторы, Затенение И Аппроксимация Абстрактных Полулинейных Дифференциальных Уравнений

Аттракторы, Затенение И Аппроксимация Абстрактных Полулинейных Дифференциальных Уравнений

A numerical algorithm based on scale-3 Haar wavelets for fractional advection dispersion equation

Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

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