scholarly journals A New Class of Coupled Systems of Nonlinear Hyperbolic Partial Fractional Differential Equations in Generalized Banach Spaces Involving the ψ–Caputo Fractional Derivative

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2412
Author(s):  
Zidane Baitiche ◽  
Choukri Derbazi ◽  
Mouffak Benchohra ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
New Class ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

The current study is devoted to investigating the existence and uniqueness of solutions for a new class of symmetrically coupled system of nonlinear hyperbolic partial-fractional differential equations in generalized Banach spaces in the sense of ψ–Caputo partial fractional derivative. Our approach is based on the Krasnoselskii-type fixed point theorem in generalized Banach spaces and Perov’s fixed point theorem together with the Bielecki norm, while Urs’s approach was used to prove the Ulam–Hyers stability of solutions of our system. Finally, some examples are provided in order to illustrate our theoretical results.

scholarly journals On the controllability of Hilfer-Katugampola fractional differential equations

2020 ◽  
Vol 24 (2) ◽  
pp. 195-204
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Fractional Differential

By employing Kuratowski's measure of noncompactness together with Sadovskii's fixed point theorem, sufficient conditions for controllability results of Hilfer-Katugampola fractional differential equations in Banach spaces are derived.

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 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.

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.

Nonlinear Riemann-Liouville fractional differential equations with nonlocal Erdelyi-Kober fractional integral conditions

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
Natthaphong Thongsalee ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractIn this paper we study a new class of Riemann-Liouville fractional differential equations subject to nonlocal Erdélyi-Kober fractional integral boundary conditions. Existence and uniqueness results are obtained by using a variety of fixed point theorems, such as Banach fixed point theorem, Nonlinear Contractions, Krasnoselskii fixed point theorem, Leray-Schauder Nonlinear Alternative and Leray-Schauder degree theory. Examples illustrating the obtained results are also presented.

scholarly journals Positive solutions of boundary value problems for p-Laplacian fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1265-1277 ◽  
Author(s):  
Fatma Fen ◽  
Ilkay Karac ◽  
Ozlem Ozen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This work is devoted to the existence of positive solutions for nonlinear fractional differential equations with p-Laplacian operator. By using five functionals fixed point theorem, the existence of at least three positive solutions are obtained. As an application, an example is presented to demonstrate our main result.

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 Existence of Positive Solutions for a Class of Delay Fractional Differential Equations with Generalization to N-Term

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Initial Conditions ◽  
Banach Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We established the existence of a positive solution of nonlinear fractional differential equationsL(D)[x(t)−x(0)]=f(t,xt),t∈(0,b]with finite delayx(t)=ω(t),t∈[−τ,0], wherelimt→0f(t,xt)=+∞, that is,fis singular att=0andxt∈C([−τ,0],ℝ≥0). The operator ofL(D)involves the Riemann-Liouville fractional derivatives. In this problem, the initial conditions with fractional order and some relations among them were considered. The analysis rely on the alternative of the Leray-Schauder fixed point theorem, the Banach fixed point theorem, and the Arzela-Ascoli theorem in a cone.

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