The general Bernstein function: application to \(\chi\)-fractional differential equations

Fractional derivatives and integrals (26A33) Other functions defined by series and integrals (33E20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Fractional ordinary differential equations (34A08)

Cites Work

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An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations
Bernstein series solution of a class of Lane-Emden type equations
Solving systems of fractional differential equations by homotopy-perturbation method
A new approach to improve the order of approximation of the Bernstein operators: theory and applications
Decomposition method for solving fractional Riccati differential equations
The solution of the Bagley-Torvik equation with the generalized Taylor collocation method
Algorithms for polynomials in Bernstein form
Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
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Application of variational iteration method to nonlinear differential equations of fractional order
A Caputo fractional derivative of a function with respect to another function
Generalized fractional derivatives and Laplace transform
Finite difference methods for Caputo-Hadamard fractional differential equations
Convergence of 2D-orthonormal Bernstein collocation method for solving 2D-mixed Volterra-Fredholm integral equations
A numerical study of fractional relaxation-oscillation equations involving \(\psi \)-Caputo fractional derivative
Solutions of differential equations in a Bernstein polynomial basis
Solving a multi-order fractional differential equation using Adomian decomposition
Error estimate of finite element/finite difference technique for solution of two-dimensional weakly singular integro-partial differential equation with space and time fractional derivatives
Collocation method and residual correction using Chebyshev series
Ritz–Galerkin method for solving an inverse heat conduction problem with a nonlinear source term via Bernstein multi-scaling functions and cubic B-spline functions
Numerical Solution for the Variable Order TimeFractional Diffusion Equation with Bernstein Polynomials
Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
On the numerical solution of stochastic quadratic integral equations via operational matrix method
On Caputo–Hadamard fractional differential equations
Solving nonlinear fractional partial differential equations using the homotopy analysis method
Fractional‐order orthogonal Bernstein polynomials for numerical solution of nonlinear fractional partial Volterra integro‐differential equations
Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials
A numerical approach based on Bernstein collocation method: application to differential Lyapunov and Sylvester matrix equations

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