scholarly journals Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Lakshman Mahto ◽  
Syed Abbas ◽  
Angelo Favini
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Logistic Model ◽  
Fixed Point Method ◽  
Uniqueness Of Solutions ◽  
Fractional Order Differential Equations ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We use Sadovskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and compliment the existing one.

scholarly journals Existence and Uniqueness for a System of Caputo-Hadamard Fractional Differential Equations with Multipoint Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
S. Nageswara Rao ◽  
Ahmed Hussein Msmali ◽  
Manoj Singh ◽  
Abdullah Ali H. Ahmadini
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

In this paper, we study existence and uniqueness of solutions for a system of Caputo-Hadamard fractional differential equations supplemented with multi-point boundary conditions. Our results are based on some classical fixed point theorems such as Banach contraction mapping principle, Leray-Schauder fixed point theorems. At last, we have presented two examples for the illustration of main results.

scholarly journals Caputo-Fabrizio fractional differential equations in Frechet spaces

2021 ◽  
Vol 13(62) (2) ◽  
pp. 373-386
Author(s):  
Said Abbas ◽  
Mouffak Benchohra ◽  
Hafsa Gorine
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Fréchet Spaces ◽  
Uniqueness Of Solutions ◽  
Darbo Fixed Point Theorem ◽  
Fractional Differential

This paper deals with some existence and uniqueness of solutions for a class of functional Caputo-Fabrizio fractional differential equations. Some applications are made of a generalization of the classical Darbo fixed point theorem for Frechet spaces associate with the concept of measure of noncompactness. The last section illustrates our results with some examples.

When do fractional differential equations have solutions that are bounded by the Mittag--Leffler function ?

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Christopher C. Tisdell
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Half Line ◽  
Growth Behaviour ◽  
Uniqueness Of Solutions ◽  
Fractional Differential ◽  
Fixed Point Methods

AbstractWhen do fractional differential equations have solutions on the half line that are bounded by the Mittag-Leffler function? This work answers the above question through fixed-point methods, providing a deeper understanding of the long term growth behaviour of solutions, in addition to advancing our knowledge on the existence and uniqueness of solutions. A YouTube video by the Author that complements this work can be found at http://tinyurl.com/FDE-ML.

scholarly journals Existence and Uniqueness of Solutions for the Cauchy-Type Problems of Fractional Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Chunhai Kou ◽  
Jian Liu ◽  
Yan Ye
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Cauchy Type ◽  
Uniqueness Of Solutions ◽  
Step Method ◽  
Fractional Differential

By using the Banach fixed point theorem and step method, we study the existence and uniqueness of solutions for the Cauchy-type problems of fractional differential equations. Meanwhile, by citing some counterexamples, it is pointed out that there exist a few defects in the proofs of the known results.

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.

scholarly journals Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

2019 ◽  
Vol 52 (1) ◽  
pp. 283-295 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Ulam Stability ◽  
Fractional Differential System ◽  
Different Types ◽  
Fractional Differential

AbstractIn this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

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