Abstract
Bu çalışmada, klasik analizden değişken katsayılı lineer diferansiyel denklemlerin
özel bir hali olan Cauchy-Euler diferansiyel denklemi ve Legendre diferansiyel
denkleminin özellikleri baz alınarak; Çarpımsal analizde değişken üslü
çarpımsal lineer diferansiyel denklemlerin özel bir hali olan çarpımsal
Cauchy-Euler diferansiyel denklemi ve çarpımsal Legendre diferansiyel
denkleminin tanımı verilmiş ve çözümleri incelenmiştir. Ayrıca çarpımsal
mertebe düşürme metodu verilmiştir.
Keywords
Çarpımsal Türev Çarpımsal Cauchy-Euler diferansiyel denklemi Çarpımsal Legendre diferansiyel denklemi
References
- Aniszewska, D., 2007. Multiplicative Runge-Kutta method, Nonlinear Dynamics, 50:265-272
- Bashirov, A.E., Mısırlı, E., ve Özyapıcı, A., 2008. Multiplicative calculus and its applications, J. Math. Anal. Appl., 337: 36-48
- Bashirov, A.E., Mısırlı, E., Tandoğdu, Y., ve Özyapıcı, A., 2011. On modeling with multiplicative differential equations, 26(4): 425-438
- Cample, D., 1999. Multiplicative calculus and student projects, Primus. Vol 9, issue 4.
- Filip, D., ve Piatecki, C., 2007. An overview on the non-newtonian calculus and its potential applications to economics, Applied Mathematics and Compututaion., 187(1): 68-78
- Filip, D., ve Piatecki, C., 2014. A non-newtonian examination of the theory of exogeneous economic growth, Mathematica Aeterna.
- Florack, L., ve Assen, H., 2012. Multiplicative Calculus in Biomedical Image Analysis, J Math.Imaging Vis., 42: 64-75
- Grossman, M.,ve Katz, R,. 1972. Non-Nowtonian Calculus, Lee Press, Pigeon Cove.
- Mora, M., Cordova-Lepe, F., ve Del-Valle, R., 2012. A non-Newtonian gradient for contour detection in images with multiplicative noise, Pattern Recognition Letters, 33: 1245-1256.
- Stanley, D., 1999. A multiplicative calculus, Primus, IX(4): 310-326.
- Rıza, M., Özyapıcı, A. ve Mısırlı, E., 2009. Multiplicative finite diference methods. Quarterly of Applied Mathematics., Vol. 67, No. 4, pp. 745-754
- Yalçın, N., Çelik, E., ve Gökdoğan, A., 2016. Multiplicative Laplace transform and its applications, Optik 127 50: 265-272.
- Yalçın, N., Çelik, E., 2018. The Solution of Multiplicative Non-Homogeneous Linear Differential Equations, Journal of Applied Mathematics and Computation, 2(1): 27-36.
- Yalçın, N., Çelik, E., 2018. Solution of multiplicative homogeneous linear differential equations with constant exponentials, New Trends in Mathematical Sciences., NTMSCI 6, No. 2, 58-67.
- Yalçın, N., 2016. Çarpımsal Türev ve Çarpımsal Lineer Diferensiyel Denklemler. Doktora Tezi, Atatürk Üniversitesi Fen Bilimleri Enstitüsü. Erzurum, 105s
Abstract
In this study, taking properties of Cauchy-Euler
differential equation and Legendre differential equation, which are particular instances
of linear differential equations with variable coefficients in classical
analysis, as a basis, definitions of multiplicative Cauchy-Euler differential
equation and multiplicative Legendre differential equation , which are types of
multiplicative linear differential equations in multiplicative analysis, are
given and also their solutions are investigated. In addition, multiplicative reduction of order method
is given.
Keywords
Multiplicative derivative Multiplicative Cauchy-Euler differential equation Multiplicative Legendre differential equation
References
- Aniszewska, D., 2007. Multiplicative Runge-Kutta method, Nonlinear Dynamics, 50:265-272
- Bashirov, A.E., Mısırlı, E., ve Özyapıcı, A., 2008. Multiplicative calculus and its applications, J. Math. Anal. Appl., 337: 36-48
- Bashirov, A.E., Mısırlı, E., Tandoğdu, Y., ve Özyapıcı, A., 2011. On modeling with multiplicative differential equations, 26(4): 425-438
- Cample, D., 1999. Multiplicative calculus and student projects, Primus. Vol 9, issue 4.
- Filip, D., ve Piatecki, C., 2007. An overview on the non-newtonian calculus and its potential applications to economics, Applied Mathematics and Compututaion., 187(1): 68-78
- Filip, D., ve Piatecki, C., 2014. A non-newtonian examination of the theory of exogeneous economic growth, Mathematica Aeterna.
- Florack, L., ve Assen, H., 2012. Multiplicative Calculus in Biomedical Image Analysis, J Math.Imaging Vis., 42: 64-75
- Grossman, M.,ve Katz, R,. 1972. Non-Nowtonian Calculus, Lee Press, Pigeon Cove.
- Mora, M., Cordova-Lepe, F., ve Del-Valle, R., 2012. A non-Newtonian gradient for contour detection in images with multiplicative noise, Pattern Recognition Letters, 33: 1245-1256.
- Stanley, D., 1999. A multiplicative calculus, Primus, IX(4): 310-326.
- Rıza, M., Özyapıcı, A. ve Mısırlı, E., 2009. Multiplicative finite diference methods. Quarterly of Applied Mathematics., Vol. 67, No. 4, pp. 745-754
- Yalçın, N., Çelik, E., ve Gökdoğan, A., 2016. Multiplicative Laplace transform and its applications, Optik 127 50: 265-272.
- Yalçın, N., Çelik, E., 2018. The Solution of Multiplicative Non-Homogeneous Linear Differential Equations, Journal of Applied Mathematics and Computation, 2(1): 27-36.
- Yalçın, N., Çelik, E., 2018. Solution of multiplicative homogeneous linear differential equations with constant exponentials, New Trends in Mathematical Sciences., NTMSCI 6, No. 2, 58-67.
- Yalçın, N., 2016. Çarpımsal Türev ve Çarpımsal Lineer Diferensiyel Denklemler. Doktora Tezi, Atatürk Üniversitesi Fen Bilimleri Enstitüsü. Erzurum, 105s
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | July 15, 2019 |
| Submission Date | August 7, 2018 |
| Acceptance Date | December 7, 2018 |
| Published in Issue | Year 2019 Volume: 9 Issue: 3 |
