scholarly journals Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 444 ◽  
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga ◽  
Maliha Rashid ◽  
Lariab Shahid ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

In this manuscript, we introduce a new notion: a Berinde type ( α , ψ ) -contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. The result, presented here, not only generalizes a number of existing results, but also unifies several ones on the topic in the literature. An application of nonlinear fractional differential equations is given.

scholarly journals On Fuzzy Extended Hexagonal b-Metric Spaces with Applications to Nonlinear Fractional Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2032
Author(s):  
Sumaiya Tasneem Zubair ◽  
Kalpana Gopalan ◽  
Thabet Abdeljawad ◽  
Bahaaeldin Abdalla
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Feasible Solution ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Fractional Differential Equations ◽  
Research Article ◽  
Fractional Differential

The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal b-metric spaces is specified as follows utilizing the function b(c,d): mhc,d,t+s+u+v+w≥mhc,e,tb(c,d)∗mhe,f,sb(c,d)∗mhf,g,ub(c,d)∗mhg,k,vb(c,d)∗mhk,d,wb(c,d) for all t,s,u,v,w>0 and c≠e,e≠f,f≠g,g≠k,k≠d. Further to that, this research attempts to provide a feasible solution for the Caputo type nonlinear fractional differential equations through effective applications of our results obtained.

scholarly journals Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations via Common Fixed-Point Techniques in Complex Valued Fuzzy Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Humaira ◽  
Muhammad Sarwar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Common Fixed Point ◽  
Fractional Differential Equations ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Complex Valued

The main purpose of this paper is to study the existence theorem for a common solution to a class of nonlinear three-point implicit boundary value problems of impulsive fractional differential equations. In this respect, we study the fuzzy version of some essential common fixed-point results from metric spaces in the newly introduced notion of complex valued fuzzy metric spaces. Also, we provide an illustrative example to demonstrate the validity of our derived results.

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.

Solvability for a couple system of nonlinear fractional differential equations in a Banach space

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Jitai Liang ◽  
Zhenhai Liu ◽  
Xuhuan Wang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Couple System ◽  
Measures Of Noncompactness ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractIn this paper, we study boundary value problems of nonlinear fractional differential equations in a Banach Space E of the following form: $\left\{ \begin{gathered} D_{0^ + }^p x(t) = f_1 (t,x(t),y(t)),t \in J = [0,1], \hfill \\ D_{0^ + }^q y(t) = f_2 (t,x(t),y(t)),t \in J = [0,1], \hfill \\ x(0) + \lambda _1 x(1) = g_1 (x,y), \hfill \\ y(0) + \lambda _2 y(1) = g_2 (x,y), \hfill \\ \end{gathered} \right. $ where D 0+ denotes the Caputo fractional derivative, 0 < p,q ≤ 1. Some new results on the solutions are obtained, by the concept of measures of noncompactness and the fixed point theorem of Mönch type.

scholarly journals Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Azizollah Babakhani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Two Dimensions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Nonlinear Fractional Differential Equations ◽  
Nonlinear Alternative ◽  
Fractional Differential

We investigate the existence and uniqueness of positive solution for system of nonlinear fractional differential equations in two dimensions with delay. Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone.

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.

scholarly journals Existence and Uniqueness Results for Two-Term Nonlinear Fractional Differential Equations via a Fixed Point Technique

2021 ◽  
Vol 2021 ◽  
pp. 1-7 ◽  
Author(s):  
H. R. Marasi ◽  
H. Aydi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Monotone Operators ◽  
Nonlinear Fractional Differential Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Wide Range ◽  
Fractional Differential

The work addressed in this paper is to ensure the existence and uniqueness of positive solutions for initial value problems for nonlinear fractional differential equations with two terms of fractional orders. By virtue of recent fixed point theorems on mixed monotone operators, we get some new straightforward results with a wide range of applications.

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.

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