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Integral solutions of nondense impulsive conformable-fractional differential equations with nonlocal condition

Bouaouid Mohamed, Hilal Khalid, Hannabou Mohamed

Journal of Applied Analysis

2021

Vol. 27, nr 2

187--197

In this paper, a class of nondense impulsive differential equations with nonlocal condition in the frame of the conformable fractional derivative is studied. The abstract results concerning the existence, uniqueness and stability of the integral solution are obtained by using the extrapolation semigroup approach combined with some fixed point theorems.

Existence and stability of impulsive coupled system of fractional integrodifferential equations

Zada Akbar, Waheed Hira, Alzabut Jehad, Wang Xiaoming

Demonstratio Mathematica

2019

Vol. 52, nr 1

296--335

In this manuscript, we deal with a class and coupled system of implicit fractional differential equations, having some initial and impulsive conditions. Existence and uniqueness results are obtained by means of Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. Hyers–Ulam stability is investigated by using classical technique of nonlinear functional analysis. Finally, we provide illustrative examples to support our obtained results.

Existence of three solutions for impulsive nonlinear fractional boundary value problems

Heidarkhani S., Ferrara M., Caristi G., Salari A.

Opuscula Mathematica

2017

Vol. 37, no. 2

281--301

In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.

Existence of three solutions for impulsive multi-point boundary value problems

Bohner M., Heidarkhani S., Salari A., Caristi G.

Opuscula Mathematica

2017

Vol. 37, no. 3

353--379

This paper is devoted to the study of the existence of at least three classical solutions for a second-order multi-point boundary value problem with impulsive effects. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results. Also by presenting an example, we ensure the applicability of our results.