Analytical approximate solutions for quadratic Riccati differential equation of fractional order using the polynomial least squares method

DOI10.1016/J.CHAOS.2017.05.002zbMath1374.34307OpenAlexW2612836241WikidataQ115359262 ScholiaQ115359262MaRDI QIDQ1677787

Bogdan Căruntu, Constantin Bota

Publication date: 13 November 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2017.05.002

zbMATH Keywords

polynomial least squares methodRiccati fractional differential equationapproximate analytical polynomial solution

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Theoretical approximation of solutions to functional-differential equations (34K07) Functional-differential equations with fractional derivatives (34K37)

Related Items (13)

Approximate solutions for the fractional order quadratic Riccati and Bagley-Torvik differential equations ⋮ Piecewise polynomial least squares method for differential equations of fractional order ⋮ Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations ⋮ Numerical solution of nonlinear fractional Riccati differential equations using compact finite difference method ⋮ Optimal control based on the polynomial least squares method ⋮ Further developments of Bessel functions via conformable calculus with applications ⋮ An algorithm for the approximate solution of the fractional Riccati differential equation ⋮ Application of Adomian decomposition method to nonlinear systems ⋮ Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations ⋮ Approximate solution for solving fractional Riccati differential equations via trigonometric basic functions ⋮ Polynomial least squares method for fractional Lane-Emden equations ⋮ Study of a nonlinear system of fractional differential equations with deviated arguments via Adomian decomposition method ⋮ Numerical solution of the conformable differential equations via shifted Legendre polynomials

Cites Work

• Numerical solutions of fractional Riccati type differential equations by means of the Bernstein polynomials
• Series solutions of non-linear Riccati differential equations with fractional order
• An efficient approach for solving the Riccati equation with fractional orders
• Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials
• Decomposition method for solving fractional Riccati differential equations
• Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations
• Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order
• Homotopy perturbation pade technique for solving fractional Riccati differential equations
• A numerical approach for fractional order Riccati differential equation using B-spline operational matrix
• Wavelet operational matrix method for solving the Riccati differential equation
• A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials
• Using an enhanced homotopy perturbation method in fractional differential equations via deforming the linear part
• Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order

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