An efficient cubic spline approximation for variable-order fractional differential equations with time delay

Yaghoobi, Shole; Moghaddam, Behrouz Parsa; Ivaz, Karim

doi:10.1007/s11071-016-3079-4

Cited by 75 publications

(29 citation statements)

References 52 publications

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“…where U is MN × 1 an unknown vector which should be calculated and GL (x, t) is the GFLFs vector that is defined in Equation (9). By integrating Equation 18two times with respect to t, we get…”

Section: Procedures Of Implementationmentioning

confidence: 99%

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Application of the modified operational matrices in multiterm variable‐order time‐fractional partial differential equations

Dehestani

Ordokhani

Razzaghi

2019

Math Methods in App Sciences

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In this paper, we present a novel discrete scheme based on Genocchi polynomials and fractional Laguerre functions to solve multiterm variable-order time-fractional partial differential equations (M-V-TFPDEs) in the large interval. In this purpose, the accurate modified operational matrices are constructed to reduce the problems into a system of algebraic equations. Also, the computational algorithm based on the method and modified operational matrices in the large interval is easily implemented. Furthermore, we discuss the error estimation of the proposed method. Ultimately, to confirm our theoretical analysis and accuracy of numerical approach, several examples are presented. KEYWORDSerror estimation, Genocchi-fractional Laguerre functions, modified operational matrices, variable-order time-fractional partial differential equations MSC CLASSIFICATION

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Section: Procedures Of Implementationmentioning

confidence: 99%

“…8 Cubic spline interpolation for variable-order fractional differential equations with time delay. 9 Legendre wavelets optimization method for variable-order fractional Poisson equation. 10 Jacobi-Gauss-Lobatto collocation method to solve the variable-order fractional Schrodinger equations.…”

Section: Introductionmentioning

confidence: 99%

Application of the modified operational matrices in multiterm variable‐order time‐fractional partial differential equations

Dehestani

Ordokhani

Razzaghi

2019

Math Methods in App Sciences

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“…Moghaddam and Machado (2017) considered spline finite difference scheme for solving nonlinear time variable order fractional partial differential equations. Yaghoobi et al (2017) discussed an efficient cubic Spline approximation for VO fractional differential equations with time delay. For more information on this topic, see (Babaei et al 2020;.…”

Section: Introductionmentioning

confidence: 99%

The novel operational matrices based on 2D-Genocchi polynomials: solving a general class of variable-order fractional partial integro-differential equations

2020

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The main purpose of this study was to introduce an efficient approximate approach for solving a general class of variable-order fractional partial integro-differential equations (VO-FPIDEs). First, the Genocchi polynomials properties and the pseudo-operational matrix of the VO-fractional derivative and fractional integration are presented. Then, to approximate an integral part of the problems, we obtain the dual pseudo-operational matrix of fractional order with a new technique. The pseudo-operational matrices of fractional order and Genocchi collocation method are applied to reduce the VO-FPIDEs to a system of algebraic equations. The error estimation indicates that the approximate solution converges to the exact solution. Also, we discuss in detail on the upper bound of error for the pseudo-operational matrix of fractional integration. In addition, to illustrate the efficiency and applicability of the approach, we present several numerical examples. Keywords Genocchi polynomials • Fractional pseudo-operational matrix • Variable-order fractional partial integro-differential equations • Mixed Riemann-Liouville integral • Variable-order fractional derivative Mathematics Subject Classification 26A33 • 33F05 • 35R09 Communicated by Agnieszka Malinowska.

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“…Compared with the earlier wind model with linear interpolation, the surface spline model could produce a more accurate wind estimate. In [22], Yaghoobi et al described a scheme based on a cubic spline interpolation which is applied to approximating the variableorder fractional integrals and is extended to solving a class of nonlinear variable-order fractional equations with time delay. Guo and Pan [18] validated this new IP scheme with twin experiments, and the results showed that the prescribed nonlinear distribution of bottom friction coefficients are better inverted with the surface spline interpolation.…”

Section: Introductionmentioning

confidence: 99%

Application of Surface Spline Interpolation Method in Parameter Estimation of a PM_2.5 Transport Adjoint Model

Zhang

2018

Mathematical Problems in Engineering

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A new method for the estimation of initial conditions (ICs) in a PM 2.5 transport adjoint model is proposed in this paper. In this method, we construct the field of ICs by interpolating values at independent points using the surface spline interpolation. Compared to the traditionally used linear interpolation, the surface spline interpolation has an advantage for reconstructing continuous smooth surfaces. The method is verified in twin experiments, and the results indicate that this method can produce better inverted ICs and less simulation errors. In practical experiments, simulation results show good agreement with the ground-level observations during the 22nd Asia-Pacific Economic Cooperation summit period, demonstrating that the new method is effective in practical application fields.

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An efficient cubic spline approximation for variable-order fractional differential equations with time delay

Cited by 75 publications

References 52 publications

Application of the modified operational matrices in multiterm variable‐order time‐fractional partial differential equations

Application of the modified operational matrices in multiterm variable‐order time‐fractional partial differential equations

The novel operational matrices based on 2D-Genocchi polynomials: solving a general class of variable-order fractional partial integro-differential equations

Application of Surface Spline Interpolation Method in Parameter Estimation of a PM_2.5 Transport Adjoint Model

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An efficient cubic spline approximation for variable-order fractional differential equations with time delay

Cited by 75 publications

References 52 publications

Application of the modified operational matrices in multiterm variable‐order time‐fractional partial differential equations

Application of the modified operational matrices in multiterm variable‐order time‐fractional partial differential equations

The novel operational matrices based on 2D-Genocchi polynomials: solving a general class of variable-order fractional partial integro-differential equations

Application of Surface Spline Interpolation Method in Parameter Estimation of a PM2.5 Transport Adjoint Model

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Application of Surface Spline Interpolation Method in Parameter Estimation of a PM_2.5 Transport Adjoint Model