ψ-Hilfer Fractional Functional Differential Equation by Picard Operator Method

2020 ◽  
Vol 9 (4) ◽  
pp. 685-702 ◽  
Author(s):  
Mohammed A. Almalahi ◽  
Mohammed S. Abdo ◽  
Satish K. Panchal
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Operator Method ◽  
Picard Operator ◽  
Functional Differential ◽  
Fractional Functional

scholarly journals Implicit functional differential equations with linear modification of the argument, via weakly Picard operator theory

2021 ◽  
Vol 37 (2) ◽  
pp. 227-234
Author(s):  
ANTON S. MUREŞAN ◽  
VIORICA MUREŞAN
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Operator Theory ◽  
Functional Differential Equations ◽  
Picard Operator ◽  
Functional Differential ◽  
Weakly Picard Operator ◽  
Theory Technique

"Let \mathbf{K}:=\mathbf{R}\text{ or }\mathbf{C},\text{ \ }0<\lambda <1 and f \in C([0,b] \times \textbf{K}^3,\textbf{K}). In this paper we use the weakly Picard operator theory technique to study the following functional-differential equation $$ y'(x)=f(x,y(x),y'(x),y(\lambda x)), x \in [0,b].$$ "

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