Existence of the Mild Solutions for Nonlocal Fractional Differential Equations of Sobolev Type with Iterated Deviating Arguments

2016 ◽  
pp. 25-37
Author(s):  
Alka Chadha ◽  
Dwijendra N. Pandey
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Mild Solutions ◽  
Sobolev Type ◽  
Deviating Arguments ◽  
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 Monotone Iterative Technique for Conformable Fractional Differential Equations with Deviating Arguments

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Huiling Chen ◽  
Shuman Meng ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Iterative Technique ◽  
Deviating Arguments ◽  
Comparison Principles ◽  
Monotone Iterative ◽  
Fractional Differential

This paper is concerned with the existence of extremal solutions for periodic boundary value problems for conformable fractional differential equations with deviating arguments. We first build two comparison principles for the corresponding linear equation with deviating arguments. With the help of new comparison principles, some sufficient conditions for the existence of extremal solutions are established by combining the method of lower and upper solutions and the monotone iterative technique. As an application, an example is presented to enrich the main results of this article.

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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