Existence results for a coupled system of ( k , φ ) " role="presentation" style="position: relative;"> ( k , φ ) ( k , φ ) (k, \varphi) -Hilfer fractional differential equations with nonlocal integro-multi-point boundary conditions

AIMS Mathematics

article

Nattapong Kamsrisuk¹  Sotiris K. Ntouyas²  Bashir Ahmad³  Ayub Samadi⁴  Jessada Tariboon¹ 

[1] Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok;Department of Mathematics, University of Ioannina;Nonlinear Analysis and Applied Mathematics ,(NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University;Department of Mathematics, Miyaneh Branch, Islamic Azad University

关键词: $ (k;    \varphi) $-Hilfer fractional derivative;    Riemann-Liouville fractional derivative;    Caputo fractional derivative;    existence;    uniqueness;    fixed point theorems;   

DOI  :  10.3934/math.2023203

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 to a nonlinear coupled systems of $ (k, \varphi) $-Hilfer fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions. We make use of the Banach contraction mapping principle to obtain the uniqueness result, while the existence results are proved with the aid of Krasnosel'ski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }} $'s fixed point theorem and Leray-Schauder alternative for the given problem. Examples demonstrating the application of the abstract results are also presented. Our results are of quite general nature and specialize in several new results for appropriate values of the parameters $ \beta_1, $ $ \beta_2, $ and the function $ \varphi $ involved in the problem at hand.

【 授权许可】

CC BY