magazinelogo

Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
Frequency: quarterly Email: jamc@hillpublisher.com
Total View: 2672272 Downloads: 493868 Citations: 374 (From Dimensions)
ArticleOpen Access http://dx.doi.org/10.26855/jamc.2018.01.003

The Solution of Multiplicative Non-Homogeneous Linear Differential Equations

Numan Yalçın1, Ercan Çelik2

1Department of Mathematical Engineering, Gümüşhane University, 29100 Gümüşhane, Turkey.

2Department of Mathematics, Atatürk University, 25100 Erzurum, Turkey.

*Corresponding author: Numan Yalçın

47
Published: March 01, 2018

Abstract

In this study, taking particular solutions of non-homogeneous differential equations with constant coefficients in classical analysis as a basis, particular solutions of non-homogeneous differential equations in multiplicative analysis are obtained by using three methods namely operator method, the method of undetermined exponentials and the method of variation of parameters with constant exponentials.

Keyword

Multiplicative non-homogeneous linear differential equations, multiplicative derivative, the operator method, the method of undetermined exponentials, the method of variation of parameters with constant exponentials

References

[1] M. Grossman, R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972.

[2] D. Stanley. A multiplicative calculus, Primus, 1999, IX(4): 310-326.

[3] D. Campbel, "Multiplicative calculus and student projects", Primus, 1999, 9(4).

[4] A. E. Bashirov, E. Mısırlı and A. Özyapıcı, Multiplicative calculus and its applications, J. Math. Anal. Appl., 2008, 337:36-48.

[5] A. E. Bashirov, E. Mısırlı, Y. Tandoğdu and A. Özyapıcı, On modeling with multiplicative differential equations, 2011,26(4): 425-438.

[6] L. Florack and H. Assen, Multiplicative Calculus in Biomedical Image Analysis, J Math Imaging Vis. 2012, 42:64-75.

[7] D. A. Filip and C. Piatecki. A non-newtonian examination of the theory of exogenous economic growth. Mathematica Aeterna, 2014. To appear.

[8] M. Mora, F. Córdova-Lepe and R. Del-Valle, A non-Newtonian gradient for contour detection in images with multiplicative noise, Pattern Recognition Letters, 2012, 33:1245-1256.

[9] D. Filip and C. Piatecki, An overview on the non-newtonian calculus and its potential applications to economics, Applied Mathematics and Computation, 2007, 187(1): 68-78.

[10] D. Aniszewska, Multiplicative Runge-Kutta method. Nonlinear Dynamics, 2007, 50:265-272.

[11] N. Yalçın, E. Çelik and A. Gökdoğan, Multiplicative Laplacetrans form and its applications, Optik, 2016, 127:9984-9995.

Copyright

© 2018 by the author(s).
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license, which permits non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited and is not modified or adapted.
https://creativecommons.org/licenses/by-nc-nd/4.0/

How to cite this paper

The Solution of Multiplicative Non-Homogeneous Linear Differential Equations

How to cite this paper: Numan Yalçın, Ercan Çelik. (2018). The Solution of Multiplicative Non-Homogeneous Linear Differential Equations. Journal of Applied Mathematics and Computation, 2(1), 27-36.

DOI: http://dx.doi.org/10.26855/jamc.2018.01.003