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The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

Author

Listed:
  • Hasan Bulut
  • Haci Mehmet Baskonus
  • Fethi Bin Muhammad Belgacem

Abstract

We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM) to some interesting nonhomogeneous fractional ordinary differential equations (FODEs). Finally, we use the solutions to form two-dimensional (2D) graphs, by using the symbolic algebra package Mathematica Program 7.

Suggested Citation

  • Hasan Bulut & Haci Mehmet Baskonus & Fethi Bin Muhammad Belgacem, 2013. "The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, September.
    • Handle: RePEc:hin:jnlaaa:203875
    DOI: 10.1155/2013/203875
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    Cited by:

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    2. Ismail, G.M. & Abdl-Rahim, H.R. & Abdel-Aty, A. & Kharabsheh, R. & Alharbi, W. & Abdel-Aty, M., 2020. "An analytical solution for fractional oscillator in a resisting medium," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Singh, Jagdev & Kumar, Devendra & Nieto, Juan J., 2017. "Analysis of an El Nino-Southern Oscillation model with a new fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 109-115.
    4. Alkahtani, B.S.T. & Atangana, A., 2016. "Controlling the wave movement on the surface of shallow water with the Caputo–Fabrizio derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 539-546.
    5. Akgül, Esra Karatas & Akgül, Ali & Yavuz, Mehmet, 2021. "New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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    7. Mamta Kapoor & Nehad Ali Shah & Salman Saleem & Wajaree Weera, 2022. "An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions," Mathematics, MDPI, vol. 10(12), pages 1-26, June.
    8. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Guerrero-Ramírez, G.V., 2016. "Triple pendulum model involving fractional derivatives with different kernels," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 248-261.
    9. Nazir, Aqsa & Ahmed, Naveed & Khan, Umar & Mohyud-din, Syed Tauseef, 2020. "On stability of improved conformable model for studying the dynamics of a malnutrition community," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    10. Eslami, Mostafa, 2016. "Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 141-148.

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