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.

Solving a Fractional-Order Differential Equation Using Rational Symmetric Contraction Mappings

2021 ◽  
Vol 5 (4) ◽  
pp. 159
Author(s):  
Hasanen A. Hammad ◽  
Praveen Agarwal ◽  
Shaher Momani ◽  
Fahad Alsharari
Keyword(s):  
Differential Equation ◽  
Fixed Points ◽  
Fractional Order ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Contraction Mappings ◽  
Continuous Mappings ◽  
Theoretical Results

The intent of this manuscript is to present new rational symmetric ϖ−ξ-contractions and infer some fixed-points for such contractions in the setting of Θ-metric spaces. Furthermore, some related results such as Suzuki-type rational symmetric contractions, orbitally Υ-complete, and orbitally continuous mappings in Θ-metric spaces are introduced. Ultimately, the theoretical results are shared to study the existence of the solution to a fractional-order differential equation with one boundary stipulation.

scholarly journals Fixed Points for Multivalued Suzuki Type (θ,R)-Contraction Mapping with Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Mujahid Abbas ◽  
Hira Iqbal ◽  
Adrian Petrusel
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Contraction Mapping ◽  
Order Differential Equation ◽  
Existence Of A Solution ◽  
First Order ◽  
Fractional Differential ◽  
Homotopy Result

In this paper, we will introduce the concept of Suzuki type multivalued (θ,R)-contraction and we will prove some fixed point results in the setting of a metric space equipped with a binary relation. Our results generalize and extend various comparable results in the existing literature. Examples are provided to support the results proved here. As an application of our results, we obtain a homotopy result, proving the existence of a solution for a second-order differential equation and for a first-order fractional differential equation.

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 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 Fixed point for F⊥-weak contraction

2021 ◽  
Vol 25 (1) ◽  
pp. 113-122
Author(s):  
Neeraj Garakoti ◽  
Joshi Chandra ◽  
Rohit Kumar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Order Differential Equation ◽  
Second Order ◽  
Weak Contraction ◽  
Second Order Differential Equation

In this paper, we establish some fixed point results for F⊥-weak contraction in orthogonal metric space and we give an application for the solution of second order differential equation.

Existence results for some impulsive partial functional fractional differential equations

2019 ◽  
Vol 13 (04) ◽  
pp. 2050074 ◽  
Author(s):  
Hadda Hammouche ◽  
Mouna Lemkeddem ◽  
Kaddour Guerbati ◽  
Khalil Ezzinbi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Differential Equations ◽  
Mild Solutions ◽  
Existence Results ◽  
Completely Continuous ◽  
Fractional Differential ◽  
Functional Differential ◽  
Fractional Functional

In this paper, we study the existence of mild solutions of impulsive evolution fractional functional differential equation of order [Formula: see text] involving a Lipschitz condition on term [Formula: see text]. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators due to Burton and Kirk.

Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses

2019 ◽  
Vol 22 (2) ◽  
pp. 495-508 ◽  
Author(s):  
Jayanta Borah ◽  
Swaroop Nandan Bora
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Mild Solution ◽  
Point Theorem ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Fractional Order Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

Abstract In this article, we establish a set of sufficient conditions for the existence of mild solution of a class of fractional differential equations with not instantaneous impulses. The results are obtained by using Banach fixed point theorem and Krasnoselskii’s fixed point theorem. An example is presented for validation of result.

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