Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations
Copyright policy )Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations
In this manuscript, we introduce a spectral technique for approximating the variable-order fractional Riccati equation (VO-FRDEs). Firstly, the solution and its space fractional derivatives is expanded as shifted Chebyshev polynomials series. Then we determine the expansion coefficients by reducing the VO-FRDEs and its conditions to a system of algebraic equations. We show the accuracy and applicability of our numerical approach through four numerical examples.
- Cairo University Egypt
- Islamic University Bangladesh
- Bani-Suef University Egypt
- Spanish National Research Council Spain
- Canadian International College Egypt
Economics, Riemann-Liouville fractional derivative, Fractional ordinary differential equations, Engineering, Differential equation, Fractional derivatives and integrals, Series (stratigraphy), Chebyshev filter, Variable (mathematics), spectral collocation method, Physics, Chebyshev equation, Numerical methods for functional-differential equations, Numerical differentiation, Fractional Derivatives, Modeling and Simulation, Physical Sciences, shifted Chebyshev polynomials, Orthogonal polynomials, Fractional Order Control, Algebraic Riccati equation, fractional calculus, Space (punctuation), Mathematical analysis, Quantum mechanics, Riccati equation, Riemann–Liouville fractional derivative of variable order, FOS: Mathematics, Spectral method, Biology, Anomalous Diffusion Modeling and Analysis, Order (exchange), Analysis and Design of Fractional Order Control Systems, QA299.6-433, Classical orthogonal polynomials, Fractional calculus, Paleontology, Statistical and Nonlinear Physics, Applied mathematics, Computer science, Operating system, Physics and Astronomy, Control and Systems Engineering, Nonlinear system, fractional Riccati differential equation, Fractional Calculus, Chebyshev polynomials, Analysis, Mathematics, Finance, Rogue Waves in Nonlinear Systems, Algebraic equation
Economics, Riemann-Liouville fractional derivative, Fractional ordinary differential equations, Engineering, Differential equation, Fractional derivatives and integrals, Series (stratigraphy), Chebyshev filter, Variable (mathematics), spectral collocation method, Physics, Chebyshev equation, Numerical methods for functional-differential equations, Numerical differentiation, Fractional Derivatives, Modeling and Simulation, Physical Sciences, shifted Chebyshev polynomials, Orthogonal polynomials, Fractional Order Control, Algebraic Riccati equation, fractional calculus, Space (punctuation), Mathematical analysis, Quantum mechanics, Riccati equation, Riemann–Liouville fractional derivative of variable order, FOS: Mathematics, Spectral method, Biology, Anomalous Diffusion Modeling and Analysis, Order (exchange), Analysis and Design of Fractional Order Control Systems, QA299.6-433, Classical orthogonal polynomials, Fractional calculus, Paleontology, Statistical and Nonlinear Physics, Applied mathematics, Computer science, Operating system, Physics and Astronomy, Control and Systems Engineering, Nonlinear system, fractional Riccati differential equation, Fractional Calculus, Chebyshev polynomials, Analysis, Mathematics, Finance, Rogue Waves in Nonlinear Systems, Algebraic equation
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