scholarly journals A Generalized Uncertain Fractional Forward Difference Equations of Riemann-Liouville Type

2019 ◽  
Vol 11 (4) ◽  
pp. 43 ◽  
Author(s):  
Pshtiwan Othman Mohammed
Keyword(s):  
Uniqueness Theorem ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Analytic Solutions ◽  
Existence And Uniqueness Theorem ◽  
Contraction Mapping Theorem ◽  
Forward Difference ◽  
Banach Contraction ◽  
Definition Of ◽  
Banach Contraction Mapping

In this paper, we firstly recall the definition of an uncertain fractional forward difference equation with Riemann-Liouvillelike forward difference. After that analytic solutions to a generalized uncertain fractional difference equations are solved by using the Picard successive iteration method. Moreover, the existence and uniqueness theorem of the solutions are proved by applying Banach contraction mapping theorem. Finally, two examples are presented to illustrate the validity of the existence and uniqueness theorem.

scholarly journals A Correlation Between Solutions of Uncertain Fractional Forward Difference Equations and Their Paths

2020 ◽  
Vol 8 ◽  
Author(s):  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed
Keyword(s):  
Fractional Calculus ◽  
Uniqueness Theorem ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Comparison Theorems ◽  
Existence And Uniqueness Theorem ◽  
Discrete Fractional Calculus ◽  
Uncertain Variables ◽  
Forward Difference ◽  
The Relationship

We consider the comparison theorems for the fractional forward h-difference equations in the context of discrete fractional calculus. Moreover, we consider the existence and uniqueness theorem for the uncertain fractional forward h-difference equations. After that the relations between the solutions for the uncertain fractional forward h-difference equations with symmetrical uncertain variables and their α-paths are established and verified using the comparison theorems and existence and uniqueness theorem. Finally, two examples are provided to illustrate the relationship between the solutions.

scholarly journals Existence and Uniqueness of Uncertain Fractional Backward Difference Equations of Riemann–Liouville Type

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Fahd Jarad ◽  
Yu-Ming Chu
Keyword(s):  
Difference Equations ◽  
Existence And Uniqueness ◽  
Lipschitz Constant ◽  
Analytic Solutions ◽  
Fractional Operators ◽  
Existence And Uniqueness Theorem ◽  
Liouville Type ◽  
Successive Iteration ◽  
Banach Contraction ◽  
Uniqueness Of The Solution

In this article, we consider the analytic solutions of the uncertain fractional backward difference equations in the sense of Riemann–Liouville fractional operators which are solved by using the Picard successive iteration method. Also, we consider the existence and uniqueness theorem of the solution to an uncertain fractional backward difference equation via the Banach contraction fixed-point theorem under the conditions of Lipschitz constant and linear combination growth. Finally, we point out some examples to confirm the validity of the existence and uniqueness of the solution.

A characterization of probability measures in terms of semi-quantum operators

2019 ◽  
Vol 22 (02) ◽  
pp. 1950009 ◽  
Author(s):  
Gabriela Popa ◽  
Aurel I. Stan
Keyword(s):  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Random Variables ◽  
Finite Family ◽  
Probability Measures ◽  
Existence And Uniqueness Theorem ◽  
Quantum Operators ◽  
Definition Of ◽  
Finite Moments

A canonical definition of the joint semi-quantum operators of a finite family of random variables, having finite moments of all orders, is given first in terms of an existence and uniqueness theorem. Then two characterizations, one for the polynomially symmetric, and another for the polynomially factorizable probability measures, having finite moments of all orders, are presented.

scholarly journals Ulam Stability of n-th Order Delay Integro-Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3029
Author(s):  
Shuyi Wang ◽  
Fanwei Meng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Mathematical Induction ◽  
Ulam Stability ◽  
Existence And Uniqueness Theorem ◽  
Integro Differential Equation ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, the Ulam stability of an n-th order delay integro-differential equation is given. Firstly, the existence and uniqueness theorem of a solution for the delay integro-differential equation is obtained using a Lipschitz condition and the Banach contraction principle. Then, the expression of the solution for delay integro-differential equation is derived by mathematical induction. On this basis, we obtain the Ulam stability of the delay integro-differential equation via Gronwall–Bellman inequality. Finally, two examples of delay integro-differential equations are given to explain our main results.

A Global Existence and Uniqueness Theorem for Ordinary Differential Equations of Generalized Order

1978 ◽  
Vol 21 (3) ◽  
pp. 267-271 ◽  
Author(s):  
Ahmed Z. Al-Abedeen ◽  
H. L. Arora
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Global Existence ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Banach Contraction ◽  
Global Existence And Uniqueness ◽  
The Banach Contraction Principle ◽  
Generalized Order

AbstractWe extend the Picard's theorem to ordinary differential equation of generalized order α, 0 ≤ α ≤ l, and prove a global existence and uniqueness theorem by using the Banach contraction principle.

scholarly journals Applications of the Bielecki renorming technique

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Mihály Bessenyei ◽  
Zsolt Páles
Keyword(s):  
Functional Analysis ◽  
Global Existence ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Existence And Uniqueness Theorem ◽  
Banach Contraction ◽  
Global Existence And Uniqueness ◽  
The Banach Contraction Principle ◽  
Elegant Proof

AbstractThe renorming technique allows one to apply the Banach Contraction Principle for maps which are not contractions with respect to the original metric. This method was invented by Bielecki and manifested in an extremely elegant proof of the Global Existence and Uniqueness Theorem for ODEs. The present paper provides further extensions and applications of Bielecki’s method to problems stemming from functional analysis and from the theory of functional equations.

scholarly journals On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 476
Author(s):  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

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