JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (7): 22-34.doi: 10.6040/j.issn.1671-9352.0.2020.668

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Existence of solutions for boundary value problems of a class of nonlinear Caputo type sequential fractional differential equations on star graphs

LI Ning, GU Hai-bo*, MA Li-na   

  1. College of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, Xinjiang, China
  • Published:2022-06-29

Abstract: The existence of solutions for a class of nonlinear Caputo type sequential fractional differential equations BVP on a star graph consisting of three nodes and two edges is investigated. By using variable transformation, the system of fractional differential equations, with mixed boundary conditions and the different domain, is transformed into an equivalent system of differential equations with the same boundary conditions and domain. Then, by using Schaefer fixed point theory and Schauder fixed point theory, a sufficient condition is obtained for the existence of solutions to boundary value problems, and by means of Banach fixed point theory, a sufficient condition is obtained for the existence and uniqueness of solutions to boundary value problems.

Key words: fractional calculus, differential equations on star graph, boundary value problem, Greens function

CLC Number: 

  • O175.14
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