A Representation of Stieltjes Integrals by Conditionally Convergent Series

1985 ◽  
pp. 731-736
Author(s):  
Fritz John
Keyword(s):  
Convergent Series ◽  
Conditionally Convergent Series

scholarly journals Time Fractional Generalized Korteweg-de Vries Equation: Explicit Series Solutions and Exact Solutions

2021 ◽  
Vol 2 (2) ◽  
pp. 62-77
Author(s):  
Rajeev Kumar ◽  
Sanjeev Kumar ◽  
Sukhneet Kaur ◽  
Shrishty Jain
Keyword(s):  
Differential Equations ◽  
Series Solution ◽  
Vries Equation ◽  
Convergent Series ◽  
De Vries ◽  
Conformable Derivatives ◽  
Graphical View ◽  
Conditionally Convergent Series ◽  
The Given ◽  
Explicit Series Solutions

In this article, an attempt is made to achieve the series solution of the time fractional generalized Korteweg-de Vries equation which leads to a conditionally convergent series solution. We have also resorted to another technique involving conversion of the given fractional partial differential equations to ordinary differential equations by using fractional complex transform. This technique is discussed separately for modified Riemann-Liouville and conformable derivatives. Convergence analysis and graphical view of the obtained solution are demonstrated in this work.

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