Approximate Solutions for Solving Nonlinear Variable-Order Fractional Riccati Differential Equations
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Abstract
In this manuscript, we introduce a spectral technique for approximating the variable-order fractional Riccati differential equation (VOFRDE). Firstly, the solution and its space fractional derivatives is expanded as shifted Chebyshev polynomials series. Then we determine the expansion coefficients by reducing the VOFRDEs and its conditions to a system of algebraic equations. We show the accuracy and applicability of our numerical approach through four numerical examples.
Description
Z .Amin, Ahmed/0000-0003-4044-3335; Abdelkawy, Mohamed/0000-0002-9043-9644
Keywords
Fractional Calculus, Riemann-Liouville Fractional Derivative Of Variable Order, Fractional Riccati Differential Equation, Spectral Collocation Method, Shifted Chebyshev Polynomials, Economics, Engineering, Differential equation, Series (stratigraphy), Chebyshev filter, Variable (mathematics), spectral collocation method, Physics, Chebyshev equation, 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, Riemann-Liouville fractional derivative, Fractional ordinary differential equations, Fractional derivatives and integrals, Numerical methods for functional-differential equations, Numerical differentiation
Fields of Science
01 natural sciences, 0103 physical sciences, 0101 mathematics
Citation
Doha, Eid H.; Abdelkawy, Mohamed A.; Amin, Ahmed Z. M.; et al., "Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations", Nonlinear Analysis-Modelling and Control, Vol. 24, No. 2, pp. 176-188, (2019).
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OpenCitations Citation Count
16
Volume
24
Issue
2
Start Page
176
End Page
188
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CrossRef : 16
Scopus : 19
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Mendeley Readers : 3
SCOPUS™ Citations
19
checked on May 29, 2026
Web of Science™ Citations
17
checked on May 29, 2026
Page Views
8
checked on May 29, 2026
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