Fixed point theorem combined with variational methods for a class of nonlinear impulsive fractional problems with derivative dependence

In this article, we deal with a class of nonlinear impulsive problems of fractional-order in which nonlinearity is due to the fractional-order derivative term. The investigation involved a fixed point theorem with a combination of variational approach and critical point theory to establish sufficien...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 2; pp. 1943 - 1953
Main Authors Khaliq, Adnan, ur Rehman, Mujeeb
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
critical points
fixed point theorem
fractional impulsive boundary value problem
variational methods
Online AccessGet full text

Cover

More Information
Summary:In this article, we deal with a class of nonlinear impulsive problems of fractional-order in which nonlinearity is due to the fractional-order derivative term. The investigation involved a fixed point theorem with a combination of variational approach and critical point theory to establish sufficient conditions for the existence of at least one solution. First, a damped problem is discussed by using the critical point theory and variational approach, then the solutions of the damped problem and the main problem are connected with the assistance of a fixed point theorem. Towards the end, to illustrate our outcomes, two examples are given.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021118