PC-Mild Solutions to Sobolev-Type Fractional Differential Equations with Non-instantaneous Impulses

2019 ◽  
Vol 16 (4) ◽  
Author(s):  
Vikram Singh ◽  
Dwijendra N. Pandey
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Mild Solutions ◽  
Sobolev Type ◽  
Fractional Differential

Nonlinear fractional differential equations of Sobolev type

2013 ◽  
Vol 37 (13) ◽  
pp. 2009-2016 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Mohammed S. Alhothuali ◽  
Bashir Ahmad ◽  
Sebti Kerbal ◽  
Mokhtar Kirane
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sobolev Type ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Nonlocal Problems for Fractional Differential Equations via Resolvent Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zhenbin Fan ◽  
Gisèle Mophou
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Mild Solutions ◽  
Resolvent Operators ◽  
Nonlocal Problems ◽  
Lipschitz Continuous ◽  
Resolvent Method ◽  
Fractional Differential ◽  
Analytic Resolvent ◽  
Cauchy Operator

We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. An example is also given to illustrate our theory.

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