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Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

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  • Ahmed Salem
  • Faris Alzahrani
  • Mohammad Alnegga

Abstract

This research paper is about the existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions. The Caputo fractional derivative is used to formulate the fractional differential equations, and the fractional integrals mentioned in the boundary conditions are due to Atangana–Baleanu and Katugampola. The existence of solution has been proven by two main fixed-point theorems: O’Regan’s fixed-point theorem and Krasnoselskii’s fixed-point theorem. By applying Banach’s fixed-point theorem, we proved the uniqueness result for the concerned problem. This research paper highlights the examples related with theorems that have already been proven.

Suggested Citation

  • Ahmed Salem & Faris Alzahrani & Mohammad Alnegga, 2020. "Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-15, February.
    • Handle: RePEc:hin:jnlmpe:7345658
    DOI: 10.1155/2020/7345658
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