A study on Langevin equation with three different fractional orders

Document Type : Research Paper


Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran


Using a novel norm that is comfy for fractional and singular differential equations the existence and uniqueness of IVP for new type nonlinear Langevin equations involving three fractional orders are discussed. This norm is a tool to measure how far a numerical solution is from the exact one. New results are based on the contraction mapping principle. Lemma 2.2 has a prominent role in proving the main theorem. The fractional derivatives are described in Caputo sense. Two examples are presented to illustrate the theory.


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Volume 12, Special Issue
December 2021
Pages 699-707
  • Receive Date: 28 July 2020
  • Revise Date: 19 October 2020
  • Accept Date: 26 December 2020