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On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative

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  • Hailong Ye
  • Rui Huang

Abstract

The purpose of this paper is to investigate the existence of solutions to the following initial value problem for nonlinear fractional differential equation involving Caputo sequential fractional derivative D c0α2D c0α1yxp-2D c0α1yx=fx,yx, x > 0, y(0) = b0, D c0α1y(0)=b1, where D c0α1, D c0α2 are Caputo fractional derivatives, 0 1, and b0,b1∈R. Local existence of solutions is established by employing Schauder fixed point theorem. Then a growth condition imposed to f guarantees not only the global existence of solutions on the interval [0, +∞), but also the fact that the intervals of existence of solutions with any fixed initial value can be extended to [0, +∞). Three illustrative examples are also presented. Existence results for initial value problems of ordinary differential equations with p‐Laplacian on the half‐axis follow as a special case of our results.

Suggested Citation

  • Hailong Ye & Rui Huang, 2015. "On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:174156
    DOI: 10.1155/2015/174156
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    References listed on IDEAS

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    1. Ahmad, Bashir & K. Ntouyas, Sotiris, 2015. "Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 615-622.
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    Cited by:

    1. Muath Awadalla, 2022. "Some Existence Results for a System of Nonlinear Sequential Fractional Differential Equations with Coupled Nonseparated Boundary Conditions," Complexity, John Wiley & Sons, vol. 2022(1).

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