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.

Caputo-Hadamard fractional differential equations in banach spaces

2018 ◽  
Vol 21 (4) ◽  
pp. 1027-1045 ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Naima Hamidi ◽  
Johnny Henderson
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Hadamard Fractional Differential Equations ◽  
Mönch’S Fixed Point Theorem ◽  
Fractional Differential

Abstract This article deals with some existence results for a class of Caputo–Hadamard fractional differential equations. The results are based on the Mönch’s fixed point theorem associated with the technique of measure of noncompactness. Two illustrative examples are presented.

scholarly journals ON THE CONTROLLABILITY OF IMPULSIVE FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

2019 ◽  
Vol 6 (1) ◽  
pp. 17-22
Author(s):  
Valliammal N ◽  
Ravichandran C
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Mönch Fixed Point Theorem

In this paper, we established the some sufficient conditions for controllability of impulsive functional integrodifferential equations with nonlocal conditions by using the measure of noncompactness and Monch fixed point theorem.

On the behavior of solutions of fractional differential equations on time scale via Hilfer fractional derivatives

2018 ◽  
Vol 21 (4) ◽  
pp. 1120-1138 ◽  
Author(s):  
Devaraj Vivek ◽  
Kuppusamy Kanagarajan ◽  
Seenith Sivasundaram
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Existence And Stability ◽  
Fractional Differential

Abstract In this paper, we study the existence and stability of Hilfer-type fractional differential equations (dynamic equations) on time scales. We obtain sufficient conditions for existence and uniqueness of solutions by using classical fixed point theorems such as Schauder's fixed point theorem and Banach fixed point theorem. In addition, Ulam stability of the proposed problem is also discussed. As in application, we provide an example to illustrate our main results.

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 Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Erdal Karapınar ◽  
Jamal Eddine Lazreg
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our 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 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.

Weak Solutions for Fractional Differential Equations via Henstock–Kurzweil–Pettis Integrals

2020 ◽  
Vol 21 (2) ◽  
pp. 135-145 ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Measure Of Noncompactness ◽  
Pettis Integral ◽  
Existence Of Weak Solutions ◽  
Fractional Differential

AbstractIn this paper, we used Henstock–Kurzweil–Pettis integral instead of classical integrals. Using fixed point theorem and weak measure of noncompactness, we study the existence of weak solutions of boundary value problem for fractional integro-differential equations in Banach spaces. Our results generalize some known results. Finally, an example is given to demonstrate the feasibility of our conclusions.

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.

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