Çarpımsal İntegral Denklemlerin Çarpımsal Kuvvet Serisi Yöntemiyle Çözümleri

Year 2023, Volume: 26 Issue: 1, 311 - 320, 27.03.2023

Arzu Bal , Numan Yalçın , Mutlu Dedetürk

https://doi.org/10.2339/politeknik.1114825

Cited By: 2

Abstract

Bu çalışmada çarpımsal integral denklem türlerinin tanımları verilmiştir. Ve değişik türdeki çarpımsal integral denklemlerinin çözümleri, çarpımsal kuvvet serisi yöntemi kullanılarak incelenmiştir. Bunlar sayısal örnekler ile desteklenmiştir.

Keywords

Çarpımsal integral denklem, çarpımsal Fredholm intergral denklem, çarpımsal Volterra integral denklem, çarpımsal Volterra-Fredholm integral denklem, çarpımsal kuvvet serisi

Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method

Abstract

In this study, definitions of types of multiplicative integral equations are given. And solutions of different types of multiplicative integral equations are investigated using the multiplicative power series method. These are supported by numerical examples.

Keywords

Multiplicative Integral Equation, Multiplicative Fredholm Integral Equation, Multiplicative Volterra Integral Equation, Multiplicative Volterra-Fredholm Integral Equation, Multiplicative power series.

References

• [1] Fredholm, I., “Sur une classe d'equations fonctionnelles”, Acta Mathematica, 27: 365–390, doi:10.1007/bf02421317, (1903).
• [2] Volterra, V. and Hostinsky, B., “Opérations Infinitésimales Linéares”, Herman, (1938).
• [3] Lovitt, W.V., “Linear Integral Equations”, Dover Publications Inc., New York, (1950).
• [4] Smithies, F., “Integral Equations”, Cambridge University Press, London, (1958).
• [5] Krasnov, M., Kiselev, K. and Makarenko, G., “Problems and Exercises in Integral Equation”, Mır Publishers, Moscow, (1971).
• [6] Kiselev, A., Makeronko, G. and Krasnov, M., (Cevdet Cerit trans.), “Problems and Exercises in Integral Equations”, Alfa Yayınları, Istanbul, (1976).
• [7] Delves, L.V. and Mohamed, J.L., “Computational Methods for Integral Equations”, Cambridge University Press, New York, (1985).
• [8] Upadhyay, S., https://www.researchgate.net/publication/283829675_Integral_equation, “Integral Equation, An Introduction” doi:10.13140/RG.2.1.2854.8569. (2015).
• [9] Brunner, H., “Volterra Integral Equations: An Introduction to Theory and Applications”, Cambridge Monographs on Applied and Computational Mathematics. Cambridge, UK: Cambridge University Press. ISBN 978-1107098725, (2017).
• [10] Durmaz, H., “Çarpımsal İntegral Denklemler Ve Çarpımsal İntegral Denklemlerin Çarpımsal Diferansiyel Denklemler İle Arasındaki İlişkisi” , MS thesis, Fen Bilimleri Enstitüsü, Gümüşhane Üniversitesi, (2019)
• [11] Güngör, N. and Durmaz, H., “Multiplicative Volterra integral equations and the relationship between multiplicative differential equations”, Ikonion Journal of Mathematics, 2(2), 9-25, (2020).
• [12] Yalçın, N., and Dedeturk, M., “Solutions of multiplicative ordinary differential equations via the multiplicative differential transform method”, Aims Mathematics, 6(4), 3393-3409, (2021).
• [13] Yalcın, N. and Dedeturk, M., “Solutions of multiplicative linear differential equations via the multiplicative power series method”, (In press).
• [14] Bashirov, A. E., Kurpınar, E. M. and Özyapıcı, A., “Multiplicative calculus and its applications”, Journal Of Mathematical Analysis And Applications, 337(1), 36-48, (2008).
• [15] Bashirov, A. E., Mısırlı, E., Tandoğdu, Y. and Özyapıcı, A., “On modeling with multiplicative differential equations”, Applied Mathematics- A Journal of Chinese Universities, 26(4), 425-438, (2011).
• [16] Çevik, C. and Özeken, Ç. C., “Completion of multiplicative metric spaces”, Gazi University Journal of Science, 29(3), (2016).
• [17] Yalçın, N., “The solutions of multiplicative Hermite differential equation and multiplicative Hermite polynomials”, Rendiconti del Circolo Matematico di Palermo Series 2, 70(1), 9-21, (2021).
• [18] Yalçın, N. and Çelik, E., “Çarpımsal Cauchy-Euler ve Legendre diferansiyel denklemi”, Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 9(3), 373-382, (2019).
• [19] Grossman, M. and Katz, R., “Non-Newtonian Calculus” Lee Press, Pigeon Cove, MA, (1972).
• [20] Misirli, E. and Gurefe, Y., “Multiplicative Adams Bashforth–Moulton methods”, Numerical Algorithms, 57(4), 425-439, (2011).
• [21] Misirli, E. and Ozyapici, A., “Exponential approximations on multiplicative calculus”, Proc. Jangjeon Math. Soc. 12(2), 227-236, (2009).
• [22] Stanley, D., “A multiplicative calculus”, Problems, Resources, and Issues in Mathematics Undergraduate Studies, 9(4), 310-326, (1999).
• [23] Yalcin, N., Celik, E. and Gokdogan, A., “Multiplicative Laplace transform and its applications”, Optik, 127(20), 9984-9995, (2016).
• [24] Yalçın, N. and Çelik, E., “The solution of multiplicative non-homogeneous linear differential equations”, J. Appl. Math. Comput, 2(1), 27-36, (2018).
• [25] Yalcin, N. and Celik, E., “Solution of multiplicative homogeneous linear differential equations with constant exponentials”, New Trends in Mathematical Sciences, 6(2), 58-67, (2018).
• [26] Gurefe, Y., “Multiplikatif Diferansiyel Denklemler ve Uygulamaları Üzerine”, Fen Bilimleri Enstitüsü, Ege Üniversitesi, (2013).