scholarly journals Solve Partial Differential Equations using the Banach Contraction Method and Improve Results Using the Trapezoidal Rule

2021 ◽  
Vol 15 (1) ◽  
pp. 69-75
Author(s):  
Ahmed Ghitheeth ◽  
Hiba Mahmood
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Trapezoidal Rule ◽  
Partial Differential ◽  
Contraction Method ◽  
Banach Contraction

scholarly journals Existence Results for a Class of Semilinear Fractional Partial Differential Equations with Delay in Banach Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Bo Zhu ◽  
Baoyan Han ◽  
Xiangyun Lin
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mild Solutions ◽  
Contraction Mapping Principle ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Banach Contraction ◽  
Banach Contraction Mapping Principle ◽  
Equations With Delay ◽  
Banach Contraction Mapping

In this paper, we consider a class of nonlinear time fractional partial differential equations with delay. We obtain the existence and uniqueness of the mild solutions for the problem by the theory of solution operator and the general Banach contraction mapping principle. We need not extra conditions to ensure the contraction constant 0<k<1. Therefore, under some general conditions, we obtain our main results.

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