Affiliation:
1. GAZI UNIVERSITY
2. MIDDLE EAST TECHNICAL UNIVERSITY
3. ANKARA UNIVERSTIY
4. ANKARA UNIVERSITY
Abstract
The purpose of this paper is to investigate some properties of multiplicative regular and periodic Sturm-Liouville problems given in general form. We first introduce regular and periodic Sturm-Liouville (S-L) problems in multiplicative analysis by using some algebraic structures. Then, we discuss the main properties such as orthogonality of different eigenfunctions of the given problems. We show that the eigenfunctions corresponding to same eigenvalues are unique modulo a constant multiplicative factor and reality of the eigenvalues of multiplicative regular S-L problems. Finally, we present some examples to illustrate our main results.
Publisher
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
Reference32 articles.
1. Aniszewska, D., Multiplicative Runge-Kutta method, Nonlinear Dynamics, 50 (2007), 265-272. https://doi.org/10.1007/s11071-006-9156-3.
2. Bashirov, A. E., Mısırlı, E., Özyapıcı, A., Multiplicative calculus and its applications, Journal of Mathematical Analysis and Applications, 337(1) (2008), 36-48. https://doi.org/10.1016/j.jmaa.2007.03.081.
3. Bashirov, A. E., Mısırlı, E., Tandoğdu, Y., Özyapıcı, A., On modeling with multiplicative differential equations, Applied Mathematics-A Journal of Chinese Universities, 26(4) (2011), 425-438. https://doi.org/10.1007/s11766-011-2767-6.
4. Bashirov, A. E., Riza, M., On complex multiplicative differentiation, TWMS Journal of Applied and Engineering Mathematics, 1(1) (2011), 75-85.
5. Campillay-Llanos, W., Guevara, F., Pinto, M., Torres, R., Differential and integral proportional calculus: how to find a primitive for f(x)=1/2πe(1/2)x2, International Journal of Mathematical Education in Science and Technology, 52(3) (2021), 463-476. https://doi.org/10.1080/0020739X.2020.1763489.