scholarly journals Approximation of mild solutions of a semilinear fractional differential equation with random noise

2020 ◽  
Vol 148 (8) ◽  
pp. 3339-3357
Author(s):  
Nguyen Huy Tuan ◽  
Erkan Nane ◽  
Donal O’Regan ◽  
Nguyen Duc Phuong
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Mild Solutions ◽  
Random Noise ◽  
Fractional Differential ◽  
Semilinear Fractional Differential Equation

Approximate solution for a 2-D fractional differential equation with discrete random noise

2020 ◽  
Vol 133 ◽  
pp. 109650 ◽  
Author(s):  
Nguyen Huy Tuan ◽  
Dumitru Baleanu ◽  
Tran Ngoc Thach ◽  
Donal O’Regan ◽  
Nguyen Huu Can
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Fractional Differential Equation ◽  
Random Noise ◽  
Fractional Differential

scholarly journals Existence and Uniqueness of the Mild Solution of an Abstract Semilinear Fractional Differential Equation with State Dependent Nonlocal Condition

2021 ◽  
Vol 45 (6) ◽  
pp. 909-923
Author(s):  
MOHAMED A. E. HERZALLAH ◽  
◽  
ASHRAF H. A. RADWAN
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Nonlocal Condition ◽  
Mild Solutions ◽  
State Dependent ◽  
Fractional Differential ◽  
Continuous Dependence Of Solutions

The purpose of this paper is to investigate the existence and uniqueness of mild solutions to a semilinear Cauchy problem for an abstract fractional differential equation with state dependent nonlocal condition. Continuous dependence of solutions on initial conditions and local ????-approximate mild solution of the considered problem will be discussed.

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