An Existence and Uniqueness Theorem for Difference Equations

1989 ◽  
Vol 20 (5) ◽  
pp. 1208-1217 ◽  
Author(s):  
Darrel Hankerson
2020 ◽  
Vol 8 ◽  
Author(s):  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed

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.


2019 ◽  
Vol 11 (4) ◽  
pp. 43 ◽  
Author(s):  
Pshtiwan Othman Mohammed

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli

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 .


2009 ◽  
Vol 42 (2) ◽  
Author(s):  
Wen-rong Li ◽  
Sui Sun Cheng

AbstractA Picard type existence and uniqueness theorem is established for iterative differential equations of the form


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