Results 1 to 10 of about 119,125 (264)
Computation, 2020 In this work, we derive the operational matrix using poly-Bernoulli polynomials. These polynomials generalize the Bernoulli polynomials using a generating function involving a polylogarithm function.
Chang Phang +2 more
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Using Mott polynomials operational matrices to optimize multi-dimensional fractional optimal control problems [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 We offer a method for solving the fractional optimal control problems of multi-dimensional. We obtain a fractional derivative and multiplication operational matrix for Mott polynomials (M-polynomials).
S.A. Alavi +3 more
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Legendre wavelet method combined with the Gauss quadrature rule for numerical solution of fractional integro-differential equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 In this paper, we use a novel technique to solve the nonlinear fractional Volterra-Fredholm integro-differential equations (FVFIDEs). To this end, the Legendre wavelets are used in conjunction with the quadrature rule for converting the problem into a ...
M. Riahi Beni
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An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2023 This study addresses the inverse issue of identifying the space-dependent heat source of the heat equation, which is stated using the optimal con-trol framework.
T. Shojaeizadeh, M. Darehmiraki
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An approximate method based on Bernstein polynomials for solving fractional PDEs with proportional delays [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2020 We apply a new method to solve fractional partial differential equations (FPDEs) with proportional delays. The method is based on expanding the unknown solution of FPDEs with proportional delays by the basis of Bernstein polynomials with unknown control ...
A. Ketabdari, M.H. Farahi, S. Effati
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Fractal and Fractional, 2021 Herein, we developed and analyzed a new fractal–fractional (FF) operational matrix for orthonormal normalized ultraspherical polynomials. We used this matrix to handle the FF Riccati differential equation with the new generalized Caputo FF derivative ...
Youssri Hassan Youssri
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Fractal and Fractional, 2023 Approximate solutions for a family of nonlinear fractional-order differential equations are introduced in this work. The fractional-order operator of the derivative are provided in the Caputo sense.
Adel Abd Elaziz El-Sayed +2 more
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Applied Mathematics in Science and Engineering, 2023 The theory of mixed fractional operators is still an uncovered area in fractional modelling. These multi-sided operators result by combining two fractional derivatives with different kernels, that is, the right-sided Caputo's and the left-sided Riemann ...
Mohamed Obeid +2 more
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Chebyshev Cardinal Wavelets for Nonlinear Volterra Integral Equations of the Second Kind [PDF]
Mathematics Interdisciplinary Research, 2022 This study concentrated on the numerical solution of a nonlinear Volterra integral equation. The approach is accorded to a type of orthogonal wavelets named the Chebyshev cardinal wavelets.
Behnam Salehi +2 more
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On the Spectrum of Hilbert Matrix Operator [PDF]
Integral Equations and Operator Theory, 2021 AbstractThe Hilbert matrix $$\begin{aligned} {\mathcal {H}}_\lambda =\left( \frac{1}{n+m+\lambda }\right) _{n,m=0}^{\infty }, \quad \lambda \ne 0,-1,-2, \ldots \, \end{aligned}$$ H
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