On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator

Advances in Difference Equations

article

Aleem, Maryam¹  Ur Rehman, Mujeeb¹  Alzabut, Jehad²  Etemad, Sina⁴  Rezapour, Shahram⁴ 

[1] School of Natural Sciences, National University of Sciences and Technology;Department of Mathematics and General Sciences, Prince Sultan University;Group of Mathematics, Faculty of Engineering, Ostim Technical University;Department of Mathematics, Azarbaijan Shahid Madani University;Department of Medical Research, China Medical University Hospital, China Medical University

关键词: Fixed point theory;    Gronwall inequality;    Stability of solutions;    The generalized Riesz fractional operator;    The generalized Caputo fractional operator;   

DOI  :  10.1186/s13662-021-03459-w

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class of fractional differential equations by using a generalized Riesz fractional operator. One can view the results of this work as a refinement for the existence theory of fractional differential equations with Riemann–Liouville, Caputo, and classical Riesz derivative. Some special cases can be derived to obtain corresponding existence results for fractional differential equations. We provide an illustrated example for the unique solution of our main result.

【 授权许可】

CC BY