scholarly journals On Fractional q-Extensions of Some q-Orthogonal Polynomials

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 97
Author(s):  
P. Njionou Sadjang ◽  
S. Mboutngam
Keyword(s):  
Differential Operator ◽  
Power Series ◽  
Difference Equation ◽  
Orthogonal Polynomials ◽  
Series Method ◽  
Power Series Method ◽  
Gaussian Type

In this paper, we introduce a fractional q-extension of the q-differential operator Dq−1 and prove some of its main properties. Next, fractional q-extensions of some classical q-orthogonal polynomials are introduced and some of the main properties of the newly-defined functions are given. Finally, a fractional q-difference equation of Gaussian type is introduced and solved by means of the power series method.

The Scope of the Power Series Method

2013 ◽  
Vol 86 (1) ◽  
pp. 56-62
Author(s):  
Richard Beals
Keyword(s):  
Power Series ◽  
Series Method ◽  
Power Series Method

A robust and efficient power series method for tracing PV curves

2015 ◽  
Author(s):  
Xiaoming Chen ◽  
David Bromberg ◽  
Xin Li ◽  
Lawrence Pileggi ◽  
Gabriela Hug
Keyword(s):  
Power Series ◽  
Series Method ◽  
Power Series Method ◽  
Efficient Power

scholarly journals A Truncation Method for Solving the Time-Fractional Benjamin-Ono Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed R. Ali
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Power Series ◽  
Fractional Order ◽  
Nonlinear Ordinary Differential Equation ◽  
Lie Symmetry ◽  
Series Method ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Bo Equation

We deem the time-fractional Benjamin-Ono (BO) equation out of the Riemann–Liouville (RL) derivative by applying the Lie symmetry analysis (LSA). By first using prolongation theorem to investigate its similarity vectors and then using these generators to transform the time-fractional BO equation to a nonlinear ordinary differential equation (NLODE) of fractional order, we complete the solutions by utilizing the power series method (PSM).

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