Boundary value problems for Hilfer type sequential fractional differential equations and inclusions involving Riemann–Stieltjes integral multi-strip boundary conditions

Advances in Difference Equations

article

Nuchpong, Cholticha¹  Ntouyas, Sotiris K.²  Samadi, Ayub⁴  Tariboon, Jessada⁵ 

[1] Thai-German Pre-engineering School, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok;Department of Mathematics, University of Ioannina;Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematices, Faculty of Science, King Abdulaziz University;Department of Mathematics, Miyaneh Branch, Islamic Azad University;Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok

关键词: Fractional differential equations;    Fractional differential inclusions;    Hilfer fractional derivative;    Riemann–Liouville fractional derivative;    Caputo fractional derivative;    Boundary value problems;    Existence and uniqueness;    Fixed point theory;   

DOI  :  10.1186/s13662-021-03424-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we study boundary value problems for sequential fractional differential equations and inclusions involving Hilfer fractional derivatives, supplemented with Riemann–Stieltjes integral multi-strip boundary conditions. Existence and uniqueness results are obtained in the single-valued case by using the classical Banach and Krasnosel’skiĭ fixed point theorems and the Leray–Schauder nonlinear alternative. In the multi-valued case an existence result is proved by using nonlinear alternative for contractive maps. Examples illustrating our results are also presented.

【 授权许可】

CC BY