scholarly journals Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative

2020 ◽  
Vol 13 (3) ◽  
pp. 723-739 ◽  
Author(s):  
Fahd Jarad ◽  
◽  
Sugumaran Harikrishnan ◽  
Kamal Shah ◽  
Kuppusamy Kanagarajan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Hilfer Fractional Derivative ◽  
Implicit Differential Equations ◽  
Existence And Stability ◽  
Stability Results

scholarly journals Nonlocal Initial Value Problem for Hybrid Generalized Hilfer-type Fractional Implicit Differential Equations

2021 ◽  
Vol 8 (1) ◽  
pp. 87-100
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Jamal Eddine Lazreg ◽  
Juan J. Nieto ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Banach Algebras ◽  
Existence Results ◽  
Initial Value ◽  
Hilfer Fractional Derivative ◽  
Implicit Differential Equations

Abstract In this paper, we prove some existence results of solutions for a class of nonlocal initial value problem for nonlinear fractional hybrid implicit differential equations under generalized Hilfer fractional derivative. The result is based on a fixed point theorem on Banach algebras. Further, examples are provided to illustrate our results.

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