scholarly journals Computing of Existence and Uniqueness Solutions for Differential Equations in Metric Spaces by Using MATLAB

2022 ◽  
Vol 10 (01) ◽  
Author(s):  
Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Topological Spaces ◽  
Topological Properties ◽  
Computer Solution ◽  
Matlab Program ◽  
Proposed Model ◽  
Is Design

A metric space is a set along with a measurement on the set, A metric actuates topological properties like open and shut sets, which lead to the investigation of more theoretical topological spaces. It also has many applications in functional analysis. The aim of this work is design and develop highly efficient algorithms that provide the existence of unique solutions to the differential equation in metric spaces using MATLAB. The quality algorithm was used and developed to solve the differential equation in metric spaces. For accurate results. The proposed model contributed to providing an integrated computer solution for all stages of the solution starting from the stage of solving differential equations in metric space and the stage of displaying and representing the results graphically in the MATLAB program

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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 Monad Metrizable Space

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1891
Author(s):  
Orhan Göçür
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Real Space ◽  
Metrizable Space ◽  
Topological Spaces ◽  
Metrizable Spaces

Do the topologies of each dimension have to be same and metrizable for metricization of any space? I show that this is not necessary with monad metrizable spaces. For example, a monad metrizable space may have got any indiscrete topologies, discrete topologies, different metric spaces, or any topological spaces in each different dimension. I compute the distance in real space between such topologies. First, the passing points between different topologies is defined and then a monad metric is defined. Then I provide definitions and some properties about monad metrizable spaces and PAS metric spaces. I show that any PAS metric space is also a monad metrizable space. Moreover, some properties and some examples about them are presented.

scholarly journals Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 143
Author(s):  
Chayut Kongban ◽  
Poom Kumam ◽  
Juan Martínez-Moreno ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Random Fixed Point ◽  
Contractive Mappings ◽  
Random Differential Equations ◽  
Contractive Maps

The main purpose in this paper is to define the modification form of random α -admissible and random α - ψ -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results.

Exponential global attractors for semigroups in metric spaces with applications to differential equations

2011 ◽  
Vol 31 (6) ◽  
pp. 1641-1667 ◽  
Author(s):  
ALEXANDRE N. CARVALHO ◽  
JAN W. CHOLEWA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Attractor ◽  
Metric Space ◽  
Metric Spaces ◽  
Global Attractors ◽  
Invariant Sets ◽  
Bounded Subset ◽  
Partial Differential ◽  
Unstable Manifolds

AbstractIn this article semigroups in a general metric space V, which have pointwise exponentially attracting local unstable manifolds of compact invariant sets, are considered. We show that under a suitable set of assumptions these semigroups possess strong exponential dissipative properties. In particular, there exists a compact global attractor which exponentially attracts each bounded subset of V. Applications of abstract results to ordinary and partial differential equations are given.

scholarly journals New Existence of Fixed Point Results in Generalized Pseudodistance Functions with Its Application to Differential Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 324 ◽  
Author(s):  
Sujitra Sanhan ◽  
Winate Sanhan ◽  
Chirasak Mongkolkeha
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Second Order ◽  
Second Order Differential Equation ◽  
Generalized Pseudodistance

The purpose of this article is to prove some existences of fixed point theorems for generalized F -contraction mapping in metric spaces by using the concept of generalized pseudodistance. In addition, we give some examples to illustrate our main results. As the application, the existence of the solution of the second order differential equation is given.

scholarly journals On the Kneser-Hukuhara property for an integro-differential equation in Banach spaces

2011 ◽  
Vol 48 (1) ◽  
pp. 51-59
Author(s):  
Aldona Dutkiewicz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Banach Spaces ◽  
Topological Properties ◽  
Measure Of Weak Noncompactness ◽  
Integro Differential Equation

Abstract In this paper we investigate some topological properties of solutions sets of some integro-differential equations in Banach spaces. Our assumptions and proofs are expressed in terms of the measure of weak noncompactness.

scholarly journals Fixed points for pairs of mappings indcomplete topological spaces

1993 ◽  
Vol 16 (2) ◽  
pp. 259-266 ◽  
Author(s):  
Troy L. Hicks ◽  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Large Class ◽  
Distance Function ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Spaces ◽  
Triangular Inequality

Several important metric space fixed point theorems are proved for a large class of non-metric spaces. In some cases the metric space proofs need only minor changes. This is surprising since the distance function used need not be symmetric and need not satisfy the triangular inequality.

Solution set for fractional differential equations with Riemann-Liouville derivative

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Yurilev Chalco-Cano ◽  
Juan Nieto ◽  
Abdelghani Ouahab ◽  
Heriberto Román-Flores
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Solution Set ◽  
Topological Properties ◽  
Initial Value ◽  
Structure Solution ◽  
Liouville Derivative ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Contractible Spaces

AbstractWe study an initial value problem for a fractional differential equation using the Riemann-Liouville fractional derivative. We obtain some topological properties of the solution set: It is the intersection of a decreasing sequence of compact nonempty contractible spaces. We extend the classical Kneser’s theorem on the structure solution set for ordinary differential equations.

scholarly journals Exciting Fixed Point Results on a Novel Space with Supportive Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hasanen A. Hammad ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Linear Equations ◽  
Topological Properties ◽  
Rlc Circuit ◽  
Complex Linear ◽  
New Space ◽  
Complex Valued ◽  
Theoretical Results

The goal of this paper is to present a new space, a complex valued controlled rectangular b -metric space (for short, υ ℂ -metric space). Some examples and topological properties of υ ℂ -metric spaces are given. Also, some related common fixed point results are discussed. Our results generalize a lot of works in this direction. Moreover, we apply the theoretical results to find a unique solution of a complex valued Atangana-Baleanu fractional integral operator and a system of complex linear equations. Finally, a numerical example to find the current that passes through the RLC circuit is illustrated.

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