Solution of fractional integro-differential equations by Bernstein polynomials

Nanware, J.A.; Goud, Parameshwari M.; Holambe, Tarachand L.

doi:10.26637/mjm0s20/0111

Cited by 3 publications

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“…In [6], Mahdy et al investigated the numerical solution of FrLIoDE by employing the least squares approach and supplementing it with a shifted Laguerre polynomial. In order to locate the numerical solution of FrLIoDE with the Caputo derivative, Nanware et al [7] used the Bernstein polynomial to solve it. The least square technique and the homotopy perturbation method were both proposed by Oyedepo et al [8] to discuss the solution to the FrIDE problem.…”

Section: Introductionmentioning

confidence: 99%

A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a Quadrature Nystrom Method

Jan,

Abdou,

Basseem

2023

Fractal Fract

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In this work, the existence and uniqueness solution of the fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position and time-space L2Ω×C0,T, T<1. The FrNMIoDE conformed to the Volterra-Hammerstein integral equation (V-HIE) of the second kind, after applying the characteristics of a fractional integral, with a general discontinuous kernel in position for the Hammerstein integral term and a continuous kernel in time to the Volterra integral (VI) term. Then, using a separation technique methodology, we developed HIE, whose physical coefficients were time-variable. By examining the system’s convergence, the product Nystrom technique (PNT) and associated schemes were employed to create a nonlinear algebraic system (NAS).

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Section: Introductionmentioning

confidence: 99%

A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a Quadrature Nystrom Method

Jan,

Abdou,

Basseem

2023

Fractal Fract

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Numerical Investigation of Fredholm Fractional Integro-differential Equations by Least Squares Method and Compact Combination of Shifted Chebyshev Polynomials

Benzahi,

Arar,

Abada

et al. 2023

J Nonlinear Math Phys

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In this study, linear Fredholm fractional integro-differential equations (FIDEs) are numerically solved, where the fractional derivative is considered in the Caputo sense. In this work, the least squares method (LSM) using a compact combination of shifted Chebyshev polynomials (SCP) of the first Kind is applied to solving a class of FIDEs. Our aim is to write the unknown function as a series of a linear combination of SCP, and then to reduce the problem to a system of linear algebraic equations, which will be solved for the unknown constants associated with the approximate solution, using MATLAB R2020a. Finally, numerical examples are presented to confirm the reliability, applicability, and efficiency of this method, in addition, various comparisons are also shown.

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Homotopy Perturbation Technique for Fractional Volterra and Fredholm Integro Differential Equations

Oyedepo

Oluwayemi

Abdullahi

et al. 2023

2023 International Conference on Science, Engineering and Business for Sustainable Development Goals (SEB-SDG)

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Solution of fractional integro-differential equations by Bernstein polynomials

Cited by 3 publications

References 0 publications

A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a Quadrature Nystrom Method

A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a Quadrature Nystrom Method

Numerical Investigation of Fredholm Fractional Integro-differential Equations by Least Squares Method and Compact Combination of Shifted Chebyshev Polynomials

Homotopy Perturbation Technique for Fractional Volterra and Fredholm Integro Differential Equations

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