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 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 Anticipated Generalized Backward Doubly Stochastic Differential Equations

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 114
Author(s):  
Tie Wang ◽  
Jiaxin Yu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Uniqueness Theorem ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Comparison Theorems ◽  
Existence And Uniqueness Theorem ◽  
New Class ◽  
Doubly Stochastic ◽  
Increasing Process

In this paper, we explore a new class of stochastic differential equations called anticipated generalized backward doubly stochastic differential equations (AGBDSDEs), which not only involve two symmetric integrals related to two independent Brownian motions and an integral driven by a continuous increasing process but also include generators depending on the anticipated terms of the solution (Y, Z). Firstly, we prove the existence and uniqueness theorem for AGBDSDEs. Further, two comparison theorems are obtained after finding a new comparison theorem for GBDSDEs.

scholarly journals On Smoothness of the Solution to the Abel Equation in Terms of the Jacobi Series Coefficients

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 81
Author(s):  
Maksim V. Kukushkin
Keyword(s):  
Uniqueness Theorem ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Weighted Space ◽  
Abel Equation ◽  
Existence And Uniqueness Theorem ◽  
Jacobi Series ◽  
Right Hand ◽  
The Right ◽  
The Relationship

In this paper, we continue our study of the Abel equation with the right-hand side belonging to the Lebesgue weighted space. We have improved the previously known result— the existence and uniqueness theorem formulated in terms of the Jacoby series coefficients that gives us an opportunity to find and classify a solution by virtue of an asymptotic of some relation containing the Jacobi series coefficients of the right-hand side. The main results are the following—the conditions imposed on the parameters, under which the Abel equation has a unique solution represented by the series, are formulated; the relationship between the values of the parameters and the solution smoothness is established. The independence between one of the parameters and the smoothness of the solution is proved.

scholarly journals Fuzzy Conformable Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Fractional Differential ◽  
Fractional Differentiability ◽  
Derivatives Of ◽  
Fuzzy Fractional Differential Equation

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

scholarly journals Link theorem and distributions of solutions to uncertain Liouville-Caputo difference equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Juan L. G. Guirao ◽  
Y. S. Hamed
Keyword(s):  
Uniqueness Theorem ◽  
Difference Equations ◽  
Special Linear ◽  
Uncertain Variables ◽  
Important Theorem ◽  
Special Case ◽  
The Uniqueness Theorem

<p style='text-indent:20px;'>We consider a class of initial fractional Liouville-Caputo difference equations (IFLCDEs) and its corresponding initial uncertain fractional Liouville-Caputo difference equations (IUFLCDEs). Next, we make comparisons between two unique solutions of the IFLCDEs by deriving an important theorem, namely the main theorem. Besides, we make comparisons between IUFLCDEs and their <inline-formula><tex-math id="M1">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths by deriving another important theorem, namely the link theorem, which is obtained by the help of the main theorem. We consider a special case of the IUFLCDEs and its solution involving the discrete Mittag-Leffler. Also, we present the solution of its <inline-formula><tex-math id="M2">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths via the solution of the special linear IUFLCDE. Furthermore, we derive the uniqueness of IUFLCDEs. Finally, we present some test examples of IUFLCDEs by using the uniqueness theorem and the link theorem to find a relation between the solutions for the IUFLCDEs of symmetrical uncertain variables and their <inline-formula><tex-math id="M3">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths.</p>

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