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Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions

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  • Jing Zhao
  • Peifen Lu
  • Yiliang Liu

Abstract

We study a boundary value problem for fractional equations involving two fractional orders. By means of a fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. In addition, we describe the dynamic behaviors of the fractional Langevin equation by using the G2 algorithm.

Suggested Citation

  • Jing Zhao & Peifen Lu & Yiliang Liu, 2013. "Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:268347
    DOI: 10.1155/2013/268347
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    References listed on IDEAS

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    1. Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-9, July.
    2. Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher‐Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    3. Bashir Ahmad & Juan J. Nieto, 2010. "Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-10, December.
    4. Wang, K.G & Tokuyama, M, 1999. "Nonequilibrium statistical description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(3), pages 341-351.
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    Cited by:

    1. Mohammed Said Souid & Zoubida Bouazza & M’hamed Bensaid & K. Sudar Mozhi & Mokhtari Mokhtar & Joshua Kiddy K. Asamoah, 2025. "Analytical Study of Variable‐Order Fractional Differential Equations With Initial and Terminal Antiperiodic Boundary Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).

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