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Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order

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  • Kashkari, Bothayna S.H.
  • Syam, Muhammed I.

Abstract

This paper is devoted to both theoretical and numerical study of Riccati equation with fractional order. A formulation to the fractional-order Legendre operational matrix of fractional integration is constructed. Existence and uniqueness results for the considered problem are provided and proved. The fractional derivative is described in the Caputo sense. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.

Suggested Citation

  • Kashkari, Bothayna S.H. & Syam, Muhammed I., 2016. "Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 281-291.
    • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:281-291
    DOI: 10.1016/j.amc.2016.06.003
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    References listed on IDEAS

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    1. Arikoglu, Aytac & Ozkol, Ibrahim, 2009. "Solution of fractional integro-differential equations by using fractional differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 521-529.
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    Cited by:

    1. Al-Mdallal, Qasem M. & Abu Omer, Ahmed S., 2018. "Fractional-order Legendre-collocation method for solving fractional initial value problems," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 74-84.
    2. Bota, Constantin & Căruntu, Bogdan, 2017. "Analytical approximate solutions for quadratic Riccati differential equation of fractional order using the Polynomial Least Squares Method," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 339-345.
    3. Haifa Bin Jebreen & Ioannis Dassios, 2022. "A Biorthogonal Hermite Cubic Spline Galerkin Method for Solving Fractional Riccati Equation," Mathematics, MDPI, vol. 10(9), pages 1-14, April.
    4. Muhammed I. Syam & Mohammed Abu Omar, 2018. "A Numerical Method for Solving a Class of Nonlinear Second Order Fractional Volterra Integro-Differntial Type of Singularly Perturbed Problems," Mathematics, MDPI, vol. 6(4), pages 1-22, March.
    5. Singh, Harendra & Srivastava, H.M., 2019. "Jacobi collocation method for the approximate solution of some fractional-order Riccati differential equations with variable coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1130-1149.
    6. Navickas, Z. & Telksnys, T. & Marcinkevicius, R. & Ragulskis, M., 2017. "Operator-based approach for the construction of analytical soliton solutions to nonlinear fractional-order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 625-634.
    7. Hosny, Khalid M. & Darwish, Mohamed M., 2022. "Novel quaternion discrete shifted Gegenbauer moments of fractional-orders for color image analysis," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    8. Atanacković, Teodor M. & Janev, Marko & Pilipović, Stevan, 2018. "Non-linear boundary value problems involving Caputo derivatives of complex fractional order," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 326-342.
    9. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    10. Ahmad Sami Bataineh & Osman Rasit Isik & Abedel-Karrem Alomari & Mohammad Shatnawi & Ishak Hashim, 2020. "An Efficient Scheme for Time-Dependent Emden-Fowler Type Equations Based on Two-Dimensional Bernstein Polynomials," Mathematics, MDPI, vol. 8(9), pages 1-17, September.

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