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An integro quadratic spline approach for a class of variable-order fractional initial value problems

Author

Listed:
  • Moghaddam, B.P.
  • Machado, J.A.T.
  • Behforooz, H.

Abstract

This paper develops a technique for the approximate solution of a class of variable-order fractional differential equations useful in the area of fluid dynamics. The method adopts a piecewise integro quadratic spline interpolation and is used in the study of the variable-order fractional Bagley–Torvik and Basset equations. The accuracy of the proposed algorithm is verified by means of illustrative examples.

Suggested Citation

  • Moghaddam, B.P. & Machado, J.A.T. & Behforooz, H., 2017. "An integro quadratic spline approach for a class of variable-order fractional initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 354-360.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:354-360
    DOI: 10.1016/j.chaos.2017.03.065
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    References listed on IDEAS

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    1. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    2. Karaaslan, Mehmet Fatih & Celiker, Fatih & Kurulay, Muhammet, 2016. "Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 51-58.
    3. West, Bruce J., 2015. "Exact solution to fractional logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 103-108.
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    Cited by:

    1. Shuqin Zhang & Lei Hu, 2019. "Unique Existence Result of Approximate Solution to Initial Value Problem for Fractional Differential Equation of Variable Order Involving the Derivative Arguments on the Half-Axis," Mathematics, MDPI, vol. 7(3), pages 1-23, March.
    2. Dumitru Baleanu & Amin Jajarmi & Mojtaba Hajipour, 2017. "A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 718-737, December.
    3. Soradi-Zeid, Samaneh & Jahanshahi, Hadi & Yousefpour, Amin & Bekiros, Stelios, 2020. "King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    5. Sarita Gajbhiye Meshram & Vijay P. Singh & Ozgur Kisi & Chandrashekhar Meshram, 2021. "Soil erosion modeling of watershed using cubic, quadratic and quintic splines," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(3), pages 2701-2719, September.

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