Existence of solutions for Caputo sequential fractional differential equations with integral boundary conditions

Document Type : Research Paper


1 Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore - 641 020, Tamilnadu, India

2 Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore - 641 407, Tamilnadu, India

3 Department of Mathematics, Phuket Rajabhat University, Phuket - 83000, Thailand


The purpose of this paper is to investigate the existence and uniqueness of solutions to the Caputo sequential fractional differential equations and inclusions with integral boundary conditions. When it comes to proving the existence of solutions, the Krasnoselskii's fixed point theorem is employed. Further, the Banach's contraction principle and the Leray-Schauder alternative are employed to prove the uniqueness of the results. Further, for the multi-valued case, we employ the nonlinear alternative for Kakutani maps, and Convitz and Nadler's fixed point theorem. We emphasize our results with numerical examples.


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Volume 14, Issue 1
January 2023
Pages 3045-3061
  • Receive Date: 21 January 2022
  • Revise Date: 04 May 2022
  • Accept Date: 10 June 2022