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The Solution of Linear Volterra Integral Equation of the First Kind with ZZ- Transform

Yıl 2021, Cilt: 6 Sayı: 3, 127 - 133, 30.12.2021

Öz

In this paper, we apply ZZ- transform to solve linear Volterra integral equation of the first kind. The several examples solve by ZZ- Transform. This means that ZZ- transform is a powerful tool for solving linear Volterra integral equations of the first kind. The Convolution theorem for the ZZ- transform has been proved. ZZ- transform for the solution of linear Volterra integral equation of the first kind submitted in application section of this paper, some applications are given to demostrate the effectiveness of proposed scheme.

Kaynakça

  • [1] Aggarwal S., Gupta AR., Singh DP., et al. Application of Laplace transform for solving population growth and decay problems. International Journal of Latest Technology in Engineering, Management & Applied Science, 7(9): 141-145, 2018.
  • [2] Aggarwal S., Singh A., Kumar A., et al. Application of Laplace transform for solving improper integrals whose integrand consisting error function. Journal of Advanced Research in Applied Mathematics and Statistics, 4(2): 1-7, 2019.
  • [3] Aboodh KS., Farah RA., Almardy IA et al. Solving delay differential equations by Aboodh transformation method. International Journal of Applied Mathematics & Statistical Sciences, 7(2): 55-64, 2018.
  • [4] Eltayeb H., and Kilicman A., A Note on the Sumudu Transforms and differential Equations, Applied Mathematical Sciences, Volume 4, no.22,1089-1098, 2010.
  • [5] Tarig M. Elzaki, The New Integral Transform “Elzaki Transform” Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 57-64, 2011.
  • [6] Aggarwal S, Chauhan R, and Sharma N., A new application of Kamal transform for solving linear Volterra integral equations. International Journal of Latest Technology in Engineering, Management & Applied Science , 7(4): 138-140, 2018.
  • [7] Mohand M. Abdelrahim M., and Tarig M. E., Elzaki Transform And Power Series Expansion On A Bulge Heaviside Step Function, Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 11, Number 3, pp. 1179-1184, 2015.
  • [8] Tarig M. E., and Salih M. E., On the Elzaki Transform and Ordinary Differential Equation With Variable Coefficients, Advances in Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 6, Number 1, pp. 13-18, 2011.
  • [9] Najafi R., Küçük GD., and Çeli̇k E., Modified iteration method for solving fractional gas dynamics equation, Mathematical Methods in the Applied Sciences 40 (4), 939-946, 2017. , [10] Zain UI Abadin Zafar, ZZ Transform Method, International Journal of Advanced Engineering and Global Technology, 4(1), 1605-1611, 2016.
  • [11] Sudhanshu A., and Nidhi S., Laplace Transform for the Solution of First Kind Linear Volterra Integral Equation, Journal of Advanced Research in Applied Mathematics and Statistics, Volume 4, Issue 3&4, Pg. No. 16-23, 2019.
Yıl 2021, Cilt: 6 Sayı: 3, 127 - 133, 30.12.2021

Öz

Kaynakça

  • [1] Aggarwal S., Gupta AR., Singh DP., et al. Application of Laplace transform for solving population growth and decay problems. International Journal of Latest Technology in Engineering, Management & Applied Science, 7(9): 141-145, 2018.
  • [2] Aggarwal S., Singh A., Kumar A., et al. Application of Laplace transform for solving improper integrals whose integrand consisting error function. Journal of Advanced Research in Applied Mathematics and Statistics, 4(2): 1-7, 2019.
  • [3] Aboodh KS., Farah RA., Almardy IA et al. Solving delay differential equations by Aboodh transformation method. International Journal of Applied Mathematics & Statistical Sciences, 7(2): 55-64, 2018.
  • [4] Eltayeb H., and Kilicman A., A Note on the Sumudu Transforms and differential Equations, Applied Mathematical Sciences, Volume 4, no.22,1089-1098, 2010.
  • [5] Tarig M. Elzaki, The New Integral Transform “Elzaki Transform” Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 57-64, 2011.
  • [6] Aggarwal S, Chauhan R, and Sharma N., A new application of Kamal transform for solving linear Volterra integral equations. International Journal of Latest Technology in Engineering, Management & Applied Science , 7(4): 138-140, 2018.
  • [7] Mohand M. Abdelrahim M., and Tarig M. E., Elzaki Transform And Power Series Expansion On A Bulge Heaviside Step Function, Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 11, Number 3, pp. 1179-1184, 2015.
  • [8] Tarig M. E., and Salih M. E., On the Elzaki Transform and Ordinary Differential Equation With Variable Coefficients, Advances in Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 6, Number 1, pp. 13-18, 2011.
  • [9] Najafi R., Küçük GD., and Çeli̇k E., Modified iteration method for solving fractional gas dynamics equation, Mathematical Methods in the Applied Sciences 40 (4), 939-946, 2017. , [10] Zain UI Abadin Zafar, ZZ Transform Method, International Journal of Advanced Engineering and Global Technology, 4(1), 1605-1611, 2016.
  • [11] Sudhanshu A., and Nidhi S., Laplace Transform for the Solution of First Kind Linear Volterra Integral Equation, Journal of Advanced Research in Applied Mathematics and Statistics, Volume 4, Issue 3&4, Pg. No. 16-23, 2019.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume VI Issue III
Yazarlar

Sıdıka Şule Şener 0000-0002-3807-7105

Ercan Celık 0000-0002-1402-1457

Erhan Özdemir Bu kişi benim 0000-0002-0415-7086

Yayımlanma Tarihi 30 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 6 Sayı: 3

Kaynak Göster

APA Şener, S. Ş., Celık, E., & Özdemir, E. (2021). The Solution of Linear Volterra Integral Equation of the First Kind with ZZ- Transform. Turkish Journal of Science, 6(3), 127-133.
AMA Şener SŞ, Celık E, Özdemir E. The Solution of Linear Volterra Integral Equation of the First Kind with ZZ- Transform. TJOS. Aralık 2021;6(3):127-133.
Chicago Şener, Sıdıka Şule, Ercan Celık, ve Erhan Özdemir. “The Solution of Linear Volterra Integral Equation of the First Kind With ZZ- Transform”. Turkish Journal of Science 6, sy. 3 (Aralık 2021): 127-33.
EndNote Şener SŞ, Celık E, Özdemir E (01 Aralık 2021) The Solution of Linear Volterra Integral Equation of the First Kind with ZZ- Transform. Turkish Journal of Science 6 3 127–133.
IEEE S. Ş. Şener, E. Celık, ve E. Özdemir, “The Solution of Linear Volterra Integral Equation of the First Kind with ZZ- Transform”, TJOS, c. 6, sy. 3, ss. 127–133, 2021.
ISNAD Şener, Sıdıka Şule vd. “The Solution of Linear Volterra Integral Equation of the First Kind With ZZ- Transform”. Turkish Journal of Science 6/3 (Aralık 2021), 127-133.
JAMA Şener SŞ, Celık E, Özdemir E. The Solution of Linear Volterra Integral Equation of the First Kind with ZZ- Transform. TJOS. 2021;6:127–133.
MLA Şener, Sıdıka Şule vd. “The Solution of Linear Volterra Integral Equation of the First Kind With ZZ- Transform”. Turkish Journal of Science, c. 6, sy. 3, 2021, ss. 127-33.
Vancouver Şener SŞ, Celık E, Özdemir E. The Solution of Linear Volterra Integral Equation of the First Kind with ZZ- Transform. TJOS. 2021;6(3):127-33.