Existence of solutions to boundary value problem for impulsive fractional differential equations

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Gabriele Bonanno ◽  
Rosana Rodríguez-López ◽  
Stepan Tersian
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Three Solutions ◽  
Fractional Order Differential Equations ◽  
Impulsive Fractional Differential Equations ◽  
Impulsive Boundary Value Problem ◽  
Fractional Differential

AbstractIn this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fractional order differential equations. The notions of classical and weak solutions are introduced. Then, existence results of at least one and three solutions are proved.

The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses

2020 ◽  
Vol 70 (3) ◽  
pp. 625-640 ◽  
Author(s):  
Mengrui Xu ◽  
Shurong Sun ◽  
Zhenlai Han
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Existence Results ◽  
Three Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Fractional Differential

AbstractIn this paper, we investigate a class of semilinear fractional differential equations with non-instantaneous impulses and integral boundary value conditions. By the method of upper and lower solutions combined with Amann three-solution theorem, existence results of at least three solutions are obtained.

Multiple solutions to boundary value problem for impulsive fractional differential equations

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Stepan Tersian
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

AbstractWe study the multiplicity of solutions for fractional differential equations subject to boundary value conditions and impulses. After introducing the notions of classical and weak solutions, we prove the existence of at least three solutions to the impulsive problem considered.

scholarly journals Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations withp-Laplacian Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Laplacian Operator ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

This paper studies the existence of solutions for a nonlinear boundary value problem of impulsive fractional differential equations withp-Laplacian operator. Our results are based on some standard fixed point theorems. Examples are given to show the applicability of our results.

A survey on impulsive fractional differential equations

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
JinRong Wang ◽  
Michal Fečkan ◽  
Yong Zhou
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Existence Results ◽  
Impulsive Fractional Differential Equations ◽  
In Series ◽  
Fractional Differential

AbstractRecently, in series of papers we have proposed different concepts of solutions of impulsive fractional differential equations (IFDE). This paper is a survey of our main results about IFDE. We present several types of such equations with various boundary value conditions as well. Concept of solutions, existence results and examples are presented. Proofs are only sketched.

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