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Existence and Uniqueness of Solutions for Fractional-Differential Equation with Boundary Condition Using Nonlinear Multi-Fractional Derivatives

Author

Listed:
  • Chanon Promsakon
  • Intesham Ansari
  • Mecieu Wetsah
  • Anoop Kumar
  • Kulandhaivel Karthikeyan
  • Thanin Sitthiwirattham
  • Xinan Hao

Abstract

In this article the existence as well as the uniqueness (EU) of the solutions for nonlinear multiorder fractional-differential equations (FDE) with local boundary conditions and fractional derivatives of different orders (Caputo and Riemann–Liouville) are covered. The existence result is derived from Krasnoselskii’s fixed point theorem and its uniqueness is shown using the Banach contraction mapping principle. To illustrate the reliability of the results, two examples are given.

Suggested Citation

  • Chanon Promsakon & Intesham Ansari & Mecieu Wetsah & Anoop Kumar & Kulandhaivel Karthikeyan & Thanin Sitthiwirattham & Xinan Hao, 2024. "Existence and Uniqueness of Solutions for Fractional-Differential Equation with Boundary Condition Using Nonlinear Multi-Fractional Derivatives," Mathematical Problems in Engineering, Hindawi, vol. 2024, pages 1-7, February.
    • Handle: RePEc:hin:jnlmpe:6844686
    DOI: 10.1155/2024/6844686
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