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Çarpımsal İntegral Denklemlerin Çarpımsal Kuvvet Serisi Yöntemiyle Çözümleri

Year 2023, , 311 - 320, 27.03.2023
https://doi.org/10.2339/politeknik.1114825

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.

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).

Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method

Year 2023, , 311 - 320, 27.03.2023
https://doi.org/10.2339/politeknik.1114825

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.

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).
There are 26 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Arzu Bal 0000-0003-1698-3032

Numan Yalçın 0000-0002-8896-6437

Mutlu Dedetürk 0000-0002-7943-9870

Publication Date March 27, 2023
Submission Date May 10, 2022
Published in Issue Year 2023

Cite

APA Bal, A., Yalçın, N., & Dedetürk, M. (2023). Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method. Politeknik Dergisi, 26(1), 311-320. https://doi.org/10.2339/politeknik.1114825
AMA Bal A, Yalçın N, Dedetürk M. Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method. Politeknik Dergisi. March 2023;26(1):311-320. doi:10.2339/politeknik.1114825
Chicago Bal, Arzu, Numan Yalçın, and Mutlu Dedetürk. “Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method”. Politeknik Dergisi 26, no. 1 (March 2023): 311-20. https://doi.org/10.2339/politeknik.1114825.
EndNote Bal A, Yalçın N, Dedetürk M (March 1, 2023) Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method. Politeknik Dergisi 26 1 311–320.
IEEE A. Bal, N. Yalçın, and M. Dedetürk, “Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method”, Politeknik Dergisi, vol. 26, no. 1, pp. 311–320, 2023, doi: 10.2339/politeknik.1114825.
ISNAD Bal, Arzu et al. “Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method”. Politeknik Dergisi 26/1 (March 2023), 311-320. https://doi.org/10.2339/politeknik.1114825.
JAMA Bal A, Yalçın N, Dedetürk M. Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method. Politeknik Dergisi. 2023;26:311–320.
MLA Bal, Arzu et al. “Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method”. Politeknik Dergisi, vol. 26, no. 1, 2023, pp. 311-20, doi:10.2339/politeknik.1114825.
Vancouver Bal A, Yalçın N, Dedetürk M. Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method. Politeknik Dergisi. 2023;26(1):311-20.
 
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