scholarly journals Existence of a solution of fractional differential equations using the fixed point technique in extended $ b $-metric spaces

2021 ◽  
Vol 7 (1) ◽  
pp. 518-535
Author(s):  
Monica-Felicia Bota ◽  
◽  
Liliana Guran ◽  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Metric Spaces ◽  
Fractional Operator ◽  
Integral Type ◽  
Existence Of A Solution ◽  
Fractional Differential ◽  
Fixed Point Technique ◽  
Cyclic Type

<abstract><p>The purpose of the present paper is to prove some fixed point results for cyclic-type operators in extended $ b $-metric spaces. The considered operators are generalized $ \varphi $-contractions and $ \alpha $-$ \varphi $ contractions. The last section is devoted to applications to integral type equations and nonlinear fractional differential equations using the Atangana-Bǎleanu fractional operator.</p></abstract>

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 Solution of Fractional Differential Equations Utilizing Symmetric Contraction

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Aftab Hussain
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Differential Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Continuous Mappings ◽  
Fractional Differential ◽  
Fixed Point Technique

The aim of this paper is to present another family of fractional symmetric α - η -contractions and build up some new results for such contraction in the context of ℱ -metric space. The author derives some results for Suzuki-type contractions and orbitally T -complete and orbitally continuous mappings in ℱ -metric spaces. The inspiration of this paper is to observe the solution of fractional-order differential equation with one of the boundary conditions using fixed-point technique in ℱ -metric space.

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 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 On An Open Question in Controlled Rectangular b-Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2239
Author(s):  
Reny George ◽  
Abdelkader Belhenniche ◽  
Sfya Benahmed ◽  
Zoran D. Mitrović ◽  
Nabil Mlaiki ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Metric Spaces ◽  
Affirmative Answer ◽  
Existence Of A Solution ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Open Question

In this paper, we give an affirmative answer to an open question posed recently by Mlaiki et al. As a consequence of our results, we get some known results in the literature. We also give an application of our results to the existence of a solution of nonlinear fractional differential equations.

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 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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