scholarly journals Some Existence Results for Impulsive Nonlinear Fractional Differential Equations with Closed Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hilmi Ergören ◽  
Adem Kiliçman
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Nonlinear Fractional Differential Equations ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We investigate some existence results for the solutions to impulsive fractional differential equations having closed boundary conditions. Our results are based on contracting mapping principle and Burton-Kirk fixed point theorem.

scholarly journals Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Naveed Ahmad ◽  
Zeeshan Ali ◽  
Kamal Shah ◽  
Akbar Zada ◽  
Ghaus ur Rahman
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Nonlocal Boundary ◽  
Dynamical Problem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We study the existence, uniqueness, and various kinds of Ulam–Hyers stability of the solutions to a nonlinear implicit type dynamical problem of impulsive fractional differential equations with nonlocal boundary conditions involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem. For stability, we utilized classical functional analysis. Also, an example is given to demonstrate our main theoretical results.

On the initial value problems for the Caputo–Fabrizio impulsive fractional differential equations

2020 ◽  
pp. 2150073
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Initial Value Problems ◽  
Initial Value ◽  
Impulsive Fractional Differential Equations ◽  
Uniqueness Results ◽  
Fractional Differential

This paper is devoted to initial value problems for impulsive fractional differential equations of Caputo–Fabrizio type fractional derivative. By means of Banach’s fixed point theorem and Schaefer’s fixed point theorem, the existence and uniqueness results are obtained. Finally, an example is given to illustrate one of the main results.

scholarly journals Existence Results for Fractional Differential Equations with Separated Boundary Conditions and Fractional Impulsive Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xi Fu ◽  
Xiaoyou Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Impulsive Conditions ◽  
Nonlinear Alternative ◽  
Fractional Differential

This paper is concerned with the fractional separated boundary value problem of fractional differential equations with fractional impulsive conditions. By means of the Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. Examples are given to illustrate the results.

scholarly journals Fractional Differential Equations with Fractional Impulsive and Nonseparated Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xi Fu ◽  
Xiaoyou Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Alternative ◽  
Schaefer Fixed Point Theorem ◽  
Fractional Differential

This paper studies the existence results for nonseparated boundary value problems of fractional differential equations with fractional impulsive conditions. By means of Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. Examples are given to illustrate the results.

scholarly journals Existence and Kummer Stability for a System of Nonlinear ϕ-Hilfer Fractional Differential Equations with Application

2021 ◽  
Vol 5 (4) ◽  
pp. 200
Author(s):  
Fatemeh Mottaghi ◽  
Chenkuan Li ◽  
Thabet Abdeljawad ◽  
Reza Saadati ◽  
Mohammad Bagher Ghaemi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Biological Systems ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

Using Krasnoselskii’s fixed point theorem and Arzela–Ascoli theorem, we investigate the existence of solutions for a system of nonlinear ϕ-Hilfer fractional differential equations. Moreover, applying an alternative fixed point theorem due to Diaz and Margolis, we prove the Kummer stability of the system on the compact domains. We also apply our main results to study the existence and Kummer stability of Lotka–Volterra’s equations that are useful to describe and characterize the dynamics of biological systems.

scholarly journals Some Existence Results for a System of Nonlinear Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Eskandar Ameer ◽  
Hassen Aydi ◽  
Hüseyin Işık ◽  
Muhammad Nazam ◽  
Vahid Parvaneh ◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Cauchy Sequence ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

In this paper, we show that a sequence satisfying a Suzuki-type JS-rational contraction or a generalized Suzuki-type Ćirić JS-contraction, under some conditions, is a Cauchy sequence. This paper presents some common fixed point theorems and an application to resolve a system of nonlinear fractional differential equations. Some examples and consequences are also given.

scholarly journals The Existence of Positive Solutions for Fractional Differential Equations with Sign Changing Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Weihua Jiang ◽  
Jiqing Qiu ◽  
Weiwei Guo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Eigenvalue Problems ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Generalized Boundary Conditions

We investigate the existence of at least two positive solutions to eigenvalue problems of fractional differential equations with sign changing nonlinearities in more generalized boundary conditions. Our analysis relies on the Avery-Peterson fixed point theorem in a cone. Some examples are given for the illustration of main results.

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