Instantaneous and Non-Instantaneous Impulsive Boundary Value Problem Involving the Generalized <i>ψ</i>-Caputo Fractional Derivative

Instantaneous and Non-Instantaneous Impulsive Boundary Value Problem Involving the Generalized <i>ψ</i>-Caputo Fractional Derivative

This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics>...

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Bibliographic Details
Main Authors: Dongping Li, Yankai Li, Fangqi Chen, Xiaozhou Feng
Format: Article
Language:English
Published: MDPI AG 2023-02-01
Series:Fractal and Fractional
Subjects:
instantaneous impulse
non-instantaneous impulse
ψ-Caputo fractional operator
variational construction
Online Access:https://www.mdpi.com/2504-3110/7/3/206
Description
Summary:This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Caputo fractional derivative with a weight. Depending on critical point theorems and some properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Caputo-type fractional integration and differentiation, the variational construction and multiplicity result of solutions are established.
ISSN:2504-3110

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