scholarly journals Antiperiodic Boundary Value Problems for Impulsive Fractional Functional Differential Equations via Conformable Derivative

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jingfeng Wang ◽  
Chuanzhi Bai
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Monotone Iterative ◽  
Lower And Upper Solution ◽  
Functional Differential ◽  
Novel Concept ◽  
Fractional Functional Differential Equations ◽  
Theoretical Results ◽  
Fractional Functional

In this paper, by using the lower and upper solution method and the monotone iterative technique, we investigate the existence of solutions to antiperiodic boundary value problems for impulsive fractional functional equations via a recent novel concept of conformable fractional derivative. An example is given to illustrate our theoretical results.

scholarly journals The Existence of Solutions for Boundary Value Problem of Fractional Functional Differential Equations with Delay

2018 ◽  
Vol 228 ◽  
pp. 01005
Author(s):  
Mengrui Xu ◽  
Yanan Li ◽  
Yige Zhao ◽  
Shurong Sun
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Contraction Mapping Principle ◽  
Alternative Theorem ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

A class of boundary value problem for fractional functional differential equation with delay $ \left\{ {\begin{array}{*{20}c} {^{C} D^{\sigma } \omega (t) = f(t,\omega _{t} ),t \in [0,\zeta ],} \\ {\omega (0) = 0,\,\omega ^{\prime}(0) = 0,\,\omega ^{\prime\prime}(\zeta ) = 1,} \\ \end{array} } \right. $ is studied, where $ 2 < \sigma \le 3,\,\,^{c} D^{\sigma } $ devote standard Caputo fractional derivative. In this article, three new criteria on existence and uniqueness of solution are obtained by Banach contraction mapping principle, Schauder fixed point theorem and nonlinear alternative theorem.

scholarly journals Boundary value problems for fractional differential equation with causal operators

2016 ◽  
Vol 1 (1) ◽  
pp. 11-22 ◽  
Author(s):  
Jingfei Jiang ◽  
Dengqing Cao ◽  
Huatao Chen
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Solution Method ◽  
Boundary Value ◽  
Monotone Iterative ◽  
Lower And Upper Solution ◽  
Fractional Differential ◽  
Causal Operators ◽  
Theoretical Results

AbstractIn this paper, we study the two-point boundary value problems for fractional differential equation with causal operator. By lower and upper solution method and the monotone iterative technique, some results for the extremal solution and quasisolutions are obtained. At last, an example is given to demonstrate the validity of assumptions and theoretical results.

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