scholarly journals Solvability for a discrete fractional mixed type sum-difference equation boundary value problem in a Banach space

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Weidong Lv ◽  
Xin-yun Zhu
Keyword(s):  
Banach Space ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Mixed Type ◽  
Boundary Value ◽  
Equation Boundary

scholarly journals Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Weidong Lv
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Equation Boundary

By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. Moreover, a suitable choice of a Banach space allows the solutions to be unbounded and two representative examples are presented to illustrate the effectiveness of the main results.

scholarly journals On the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Lili Kong ◽  
Huiqin Chen ◽  
Luping Li ◽  
Shugui Kang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Fractional Difference ◽  
Equation Boundary ◽  
Fractional Difference Equation

In this paper, we introduce the application of three fixed point theorem by discussing the existence of three positive solutions for a class of Caputo fractional difference equation boundary value problem. We establish the condition of the existence of three positive solutions for this problem.

scholarly journals Existence of Solutions for Boundary Value Problem of a Caputo Fractional Difference Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Zhiping Liu ◽  
Shugui Kang ◽  
Huiqin Chen ◽  
Jianmin Guo ◽  
Yaqiong Cui ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Discrete Fractional Calculus ◽  
Fractional Difference ◽  
Equation Boundary ◽  
Fractional Difference Equation

We investigate the existence of solutions for a Caputo fractional difference equation boundary value problem. We use Schauder fixed point theorem to deduce the existence of solutions. The proofs are based upon the theory of discrete fractional calculus. We also provide some examples to illustrate our main results.

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