Existence of solutions for Caputo fractional iterative equations under several boundary value conditions

AIMS Mathematics

article

Cuiying Li¹  Rui Wu²  Ranzhuo Ma¹ 

[1] Department of Mathematics, Bohai University;Department of Mathematics, Changchun University of Finance and Economics

关键词: existence;    uniqueness;    Caputo fractional;    iterative equation;   

DOI  :  10.3934/math.2023015

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, we investigate the existence and uniqueness of solutions for nonlinear quadratic iterative equations in the sense of the Caputo fractional derivative with different boundary conditions. Under a one-sided-Lipschitz condition on the nonlinear term, the existence and uniqueness of a solution for the boundary value problems of Caputo fractional iterative equations with arbitrary order is demonstrated by applying the Leray-Schauder fixed point theorem and topological degree theory, where the solution for the case of fractional order greater than 1 is monotonic. Then, the existence and uniqueness of a solution for the period and integral boundary value problems of Caputo fractional quadratic iterative equations in $ R^N $ are also demonstrated. Furthermore, the well posedness of the control problem of a nonlinear iteration system with a disturbance is established by applying set-valued theory, and the existence of solutions for a neural network iterative system is guaranteed. As an application, an example is provided at the end.

【 授权许可】

CC BY