Existence and uniqueness of solution of Caputo fractional differential equations

2012 ◽  
Author(s):  
Lakshman Mahto ◽  
Syed Abbas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Some new generalizations of $ F- $contraction type mappings that weaken certain conditions on Caputo fractional type differential equations

2021 ◽  
Vol 6 (11) ◽  
pp. 12718-12742
Author(s):  
Naeem Saleem ◽  
◽  
Mi Zhou ◽  
Shahid Bashir ◽  
Syed Muhammad Husnine ◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Contraction Type ◽  
Fractional Type

<abstract><p>In this paper, firstly, we introduce some new generalizations of $ F- $contraction, $ F- $Suzuki contraction, and $ F- $expanding mappings. Secondly, we prove the existence and uniqueness of the fixed points for these mappings. Finally, as an application of our main result, we investigate the existence of a unique solution of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order (1, 2).</p></abstract>

scholarly journals Some Higher-Degree Lacunary Fractional Splines in the Approximation of Fractional Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 422
Author(s):  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Juan L. G. Guirao ◽  
Y. S. Hamed
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Real Life ◽  
Spline Functions ◽  
Spline Method ◽  
Unique Positive Solution ◽  
Caputo Fractional Differential Equations ◽  
Recent Developments ◽  
Fractional Differential

In this article, we begin by introducing two classes of lacunary fractional spline functions by using the Liouville–Caputo fractional Taylor expansion. We then introduce a new higher-order lacunary fractional spline method. We not only derive the existence and uniqueness of the method, but we also provide the error bounds for approximating the unique positive solution. As applications of our fundamental findings, we offer some Liouville–Caputo fractional differential equations (FDEs) to illustrate the practicability and effectiveness of the proposed method. Several recent developments on the the theory and applications of FDEs in (for example) real-life situations are also indicated.

scholarly journals On Some Existence and Uniqueness Results for a Class of Equations of Order0<α≤1on Arbitrary Time Scales

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Abdourazek Souahi ◽  
Assia Guezane-Lakoud ◽  
Rabah Khaldi
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Arbitrary Time ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

This paper investigates the existence and uniqueness of solution for a class of nonlinear fractional differential equations of fractional order0<α≤1in arbitrary time scales. The results are established using extensions of Krasnoselskii-Krein, Rogers, and Kooi conditions.

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