scholarly journals A Hybrid Contraction that Involves Jaggi Type

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 715
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Hybrid Type ◽  
Fractional Differential ◽  
The Given ◽  
Type Contraction

In this manuscript, we aim to provide a new hybrid type contraction that is a combination of a Jaggi type contraction and interpolative type contraction in the framework of complete metric spaces. We investigate the existence and uniqueness of such a hybrid contraction in separate theorems. We consider a solution to certain fractional differential equations as an application of the given results. In addition, we provide an example to indicate the genuineness of the given results.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

scholarly journals A study of symmetric contractions with an application to generalized fractional differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aftab Hussain ◽  
Fahd Jarad ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fractional Differential ◽  
Generalized Fractional Derivative ◽  
Fractional Boundary Value Problems

AbstractThis article proposes four distinct kinds of symmetric contraction in the framework of complete F-metric spaces. We examine the condition to guarantee the existence and uniqueness of a fixed point for these contractions. As an application, we look for the solutions to fractional boundary value problems involving a generalized fractional derivative known as the fractional derivative with respect to another function.

Impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces

2021 ◽  
Vol 19 (1) ◽  
pp. 363-372
Author(s):  
Jamal Eddine Lazreg ◽  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Erdal Karapınar
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Metric Spaces ◽  
The Subject ◽  
Fractional Differential ◽  
Type Contraction

Abstract We deal with some impulsive Caputo-Fabrizio fractional differential equations in b b -metric spaces. We make use of α - ϕ \alpha \text{-}\phi -Geraghty-type contraction. An illustrative example is the subject of the last section.

scholarly journals Impulsive Coupled System of Fractional Differential Equations with Caputo–Katugampola Fuzzy Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Leila Sajedi ◽  
Nasrin Eghbali ◽  
Hassen Aydi
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
The Given ◽  
Stability Results ◽  
Rassias Stability

In this article, we investigate the existence, uniqueness, and different kinds of Ulam–Hyers stability of solutions of an impulsive coupled system of fractional differential equations by using the Caputo–Katugampola fuzzy fractional derivative. We applied the Perov-type fixed point theorem to prove the existence and uniqueness of the proposed system. Furthermore, the Ulam–Hyers–Rassias stability and Ulam–Hyers–Rassias–Mittag-Leffler’s stability results for the given system are discussed.

scholarly journals Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1168
Author(s):  
Hanadi Zahed ◽  
Hoda A. Fouad ◽  
Snezhana Hristova ◽  
Jamshaid Ahmad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Integral Boundary ◽  
Complete Metric Spaces ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

The main objective of this paper is to introduce the ( α , β )-type ϑ -contraction, ( α , β )-type rational ϑ -contraction, and cyclic ( α - ϑ ) contraction. Based on these definitions we prove fixed point theorems in the complete metric spaces. These results extend and improve some known results in the literature. As an application of the proved fixed point Theorems, we study the existence of solutions of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order in (1,2).

scholarly journals Terminal Value Problem for Implicit Katugampola Fractional Differential Equations in b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Salim Krim ◽  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fractional Differential ◽  
Terminal Value Problem ◽  
Type Contraction ◽  
Implicit Fractional Differential Equations

This manuscript deals with a class of Katugampola implicit fractional differential equations in b -metric spaces. The results are based on the α − φ -Geraghty type contraction and the fixed point theory. We express an illustrative example.

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