8 research outputs found
Identities and relations associated with Milne-Thomson type polynomials and numbers
No full textInternational Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 -- 13 September 2018 through 18 September 2018 -- -- 149843In this paper, by using generating functions with the analysis of their Cauchy product, we derive some identities and relations associated with the Milne-Thomson type polynomials and numbers. © 2019 Author(s)
Series representation for Milne-Thomson type polynomials with approach of Mellin transformation
No full textInternational Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 -- 13 September 2018 through 18 September 2018 -- -- 149843The goal of this paper is to apply the Mellin transformation to the generating functions for the Milne-Thomson type polynomials and to derive series representation for these polynomials. Moreover, we present some applications related to our results. © 2019 Author(s)
Partial Derivative Equations and Identities for Hermite-Based Peters-Type Simsek Polynomials and Their Applications
No full textThe objective of this paper is to investigate Hermite-based Peters-type Simsek polynomials with generating functions. By using generating function methods, we determine some of the properties of these polynomials. By applying the derivative operator to the generating functions of these polynomials, we also determine many of the identities and relations that encompass these polynomials and special numbers and polynomials. Moreover, using integral techniques, we obtain some formulas covering the Cauchy numbers, the Peters-type Simsek numbers and polynomials of the first kind, the two-variable Hermite polynomials, and the Hermite-based Peters-type Simsek polynomials
Identities related to special polynomials and combinatorial numbers
No full textThe aim of this paper is to give some new identities and relations related to
the some families of special numbers such as the Bernoulli numbers, the
Euler numbers, the Stirling numbers of the first and second kinds, the
central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?)
which are given Simsek [31]. Our method is related to the functional
equations of the generating functions and the fermionic and bosonic p-adic
Volkenborn integral on Zp. Finally, we give remarks and comments on our
results.</jats:p
Homotopy analysis method for space- and time-fractional KdV equation
No full textPurpose - The purpose of this paper is to present numerical solutions for the space- and time-fractional Korteweg-de Vries (KdV) equation using homotopy analysis method (HAM). The space and time-fractional derivatives are described in the Caputo sense. The paper witnesses the extension of HAM for fractional KdV equations. Design/methodology/approach - This paper presents numerical solutions for the space- and time-fractional KdV equation using HAM. The space and time-fractional derivatives are described in the Caputo sense. Findings - In this paper, the application of homotopy analysis method was extended to obtain explicit and numerical solutions of the time- and space-fractional KdV equation with initial conditions. The homotopy analysis method was clearly a very efficient and powerful technique in finding the solutions of the proposed equations. Originality/value - In this paper, the application of HAM was extended to obtain explicit and numerical solutions of the time- and space-fractional KdV equation with initial conditions. The HAM was clearly very efficient and powerful technique in finding the solutions of the proposed equations. The obtained results demonstrate the reliability of the algorithm and its wider applicability to fractional nonlinear evolution equations. Finally, the recent appearance of nonlinear fractional differential equations as models in some fields such as the thermal diffusion in fractal media makes it necessary to investigate the method of solutions for such equations and the authors hope that this paper is a step in this direction
