A numerical method for solving fractional delay differential equations based on the operational matrix method

Syam, Muhammed I.; Sharadga, Mwaffag; Hashim, Ishak

doi:10.1016/j.chaos.2021.110977

Cited by 21 publications

(15 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The analytical solution to the linear model given above is z(t) = t + 𝛼t 1.5 . This model has been discussed in Syam et al [35]. By applying the numerical scheme introduced in Section 3, we convert the linear equation to the matrix equation…”

Section: Numerical Experiments and Discussionmentioning

confidence: 99%

A shifted Chebyshev operational matrix method for pantograph‐type nonlinear fractional differential equations

Yang,

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

In this study, we investigate and analyze an approximation of the Chebyshev polynomials for pantograph‐type fractional‐order differential equations. First, we construct the operational matrices of pantograph and Caputo fractional derivatives using Chebyshev interpolation. Then, the obtained matrices are utilized to approximate the fractional derivative. We also provide a detailed convergence analysis in terms of the weighted square norm. Finally, we describe and discuss the results of three numerical experiments conducted to confirm the applicability and accuracy of the computational scheme.

show abstract

Section: Numerical Experiments and Discussionmentioning

confidence: 99%

A shifted Chebyshev operational matrix method for pantograph‐type nonlinear fractional differential equations

Yang,

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…with Y(0) = 1 and Y(t) = 1 + ν t 2 as the exact solution. Syam et al (2021) considered this problem and applied the modified operational matrix method (MOMM) for getting the numerical solution. Table 1 compares the absolute errors of Y(t) at {ρ, σ } = {0, 0} with distinct values of ν against the numerical results given by the MOMM (Syam et al 2021).…”

Section: Stability Analysismentioning

confidence: 99%

Robust spectral treatment for time-fractional delay partial differential equations

2023

View full text Add to dashboard Cite

Fractional delay differential equations (FDDEs) and time-fractional delay partial differential equations (TFDPDEs) are the focus of the present research. The FDDEs is converted into a system of algebraic equations utilizing a novel numerical approach based on the spectral Galerkin (SG) technique. The suggested numerical technique is likewise utilized for TFDPDEs. In terms of shifted Jacobi polynomials, suitable trial functions are developed to fulfill the initial-boundary conditions of the main problems. According to the authors, this is the first time utilizing the SG technique to solve TFDPDEs. The approximate solution of five numerical examples is provided and compared with those of other approaches and with the analytic solutions to test the superiority of the proposed method.

show abstract

“…In this example, the following form of fractional order differential equation with a proportional delay is considered [47]:…”

Section: Examplementioning

confidence: 99%

“…We solve the given problem (31) for µ = 1/2 and by choosing σ = 1/2, m = 4. A comparison between the acquired absolute errors of the present technique and the modified operational matrix method (MOMM) [47] are presented in Table 6. From these findings, we can conclude that the present method is very efficient even for small numbers m. In Figure 11, we illustrate the exact solution and the approximate solution acquired by using the given approach for the problem (31).…”

Section: Examplementioning

confidence: 99%

“…For most FDDEs, exact solutions are not known. Therefore, various numerical techniques such as the Legendre wavelet method [42], the Chebyshev operational matrix method [43], the Bernoulli wavelets method [44], the shifted Gegenbauer-Gauss collocation method [45], the Haar wavelet collocation method [46], the modified operational matrix method [47], the discontinuous Galerkin method [48], spectral methods [49], etc., have been developed and applied to provide approximate solutions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Simulation of Fractional Delay Differential Equations Using the Operational Matrix of Fractional Integration for Fractional-Order Taylor Basis

Avcı

2021

Fractal Fract

View full text Add to dashboard Cite

In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures.

show abstract

A numerical method for solving fractional delay differential equations based on the operational matrix method

Cited by 21 publications

References 14 publications

A shifted Chebyshev operational matrix method for pantograph‐type nonlinear fractional differential equations

A shifted Chebyshev operational matrix method for pantograph‐type nonlinear fractional differential equations

Robust spectral treatment for time-fractional delay partial differential equations

Numerical Simulation of Fractional Delay Differential Equations Using the Operational Matrix of Fractional Integration for Fractional-Order Taylor Basis

Contact Info

Product

Resources

About