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Volterra integral denklemlerinin ve Volterra integro-diferensiyel denklemlerinin G_r-dönüşümü kullanılarak çözümü

Year 2025, Volume: 6 Issue: 1, 102 - 112, 29.05.2025

Adil Mısır , İslam Alsalih

https://doi.org/10.63716/guffd.1548492

Abstract

Volterra integral denklemleri ve Volterra integro-diferensiyel denklemleri, birçok farklı mühendislik ve bilimsel problemin oldukça genel temsilleri olarak karşımıza çıkmaktadır. Bu makalede yazarlar, lineer Volterra integral denklemlerini ve lineer Volterra integro-diferensiyel denklemlerini çözmek için yeni geliştirilen ve G_r-dönüşümü olarak adlandırılan bir hesaplama algoritmasını tanıtmaktadırlar. Daha sonra birkaç örnekle G_r-dönüşümünün her iki denklem türünü çözmedeki verimliliğini göstermektedirler.

Keywords

Volterra integral denklemleri Volterra integro-differensiyel denklemleri G_r-dönüşümü

References

  • Linz, P. (1974). A simple approximation method for solving Volterra integro-differential equations of the first kind. IMA Journal of Applied Mathematics, 14(2), 211–215.
  • Çimen, E. (2018). A computational method for Volterra integro-diferentialequation. Erzincan Fen Bilimleri Enstitüsü Dergisi, 11(3), 347–352.
  • Ajileye, G., Amoo S.A. (2023). Numerical solution to Volterra integro-differential equations using collocation approximation. Mathematics and Computational Sciences, 4(1), 1–8.
  • Zhou, H., Wang, Q., (2019). The Nystrom method and convergence analysis for system of Fredholm integral equations. Fundamental Journal of Mathematics and Applications, 2(1), 28-32.
  • Zhou, H., Wang, Q., (2019). Two-Grid iterative method for a class of Fredholm functional integral equations based on the radial basis function interpolation. Fundamental Journal of Mathematics and Applications, 2(2), 117-122.
  • Dafemos, C. M. (1970). An abstract Volterra equation with applications to linear viscoelasticity. Journal of Differential Equations, 7(3), 554–569.
  • Levinson, N. (1960). A nonlinear Volterra equation arising in the theory of superfluidity. Journal of Mathematical Analysis and Applications, 1(1), 1–11.
  • Shilepsky, C. C. (1974). The asymptotic behavior of an integral equation with an application to Volterra’s population equation. Journal of Mathematical Analysis and Applications, 48(3), 764–779.
  • Swick, K. E. (1981). A nonlinear model for human population dynamics. SIAM Journal on Applied Mathematics, 40(2), 266–278.
  • Distefano, N. (1968). A Volterra integral equation in the stability of some linear hereditary phenomena. Journal of Mathematical Analysis and Applications, 23(2), 365–383.
  • Philip, J. R. (1966). Some integral equations in geometrical probability. Biometrika, 53(3–4), 365–374.
  • Feller, W. (1941). On the integral equation of renewal theory. The Annals of Mathematical Statics, 12(3), 243–267.
  • Wang, F. J. S. (1978). Asymptotic behavior of some deterministic epidemic models. SIAM Journal on Mathematical Analysis, 9(3), 529–534.
  • Lin, S. P. (1975). Damped vibration of a string. Journal of Fluid Mechanics, 72(4), 787–797.
  • Rogers, T. G., Lee, E. H. (1964). The cylinder problem in viscoelastic stress analysis. Quarterly of Applied Mathematics, 22(2), 117–131.
  • Goldsmith, P. L. (1967). The calculation of true particle size distributions from the sizes observed in a thin slice. British Journal of Applied Physics, 18(6), 813.
  • Raisinghania, M. D. (2007). Integral equations and boundary value problems. New Delhi. S. Chand Publishing.
  • Rahman, M. (2007). Integral Equations and Their Applications. Boston. WIT press.
  • Polyanin, P., Manzhirov, A. V. (2008). Handbook of Integral Equations. London: Chapman and Hall/CRC.
  • Wazwaz, A. M. (2011). Linear and nonlinear integral equations. Berlin. Springer.
  • Pipkin, A. C. (1991). A Course on Integral Equations. New York Berlin Heidelberg. Springer Science & Business Media, 9.
  • Bitsadze, A. V. (1995). Integral Equations of First Kind. Singapore. World Scientific, 7.
  • Hackbusch, W. (1995). Integral Equation Theory and Numerical Treatment. Basel. Birkhauser press.
  • Aggarwal, S., Gupta, A. R., Sharma, S. D. (2019). A new application of Shehu transform for handling Volterra integral equations of first kind. International Journal of Research in Advent Technology, 7(4), 439–445.
  • Aggarwal, S., Sharma, N., Chauhan, R. (2018). Application of Kamal transform for solving linear Volterra integral equations of first kind. International Journal of Research in Advent Technology, 6(8), 2081–2088.
  • Higazy, M., Aggarwal, S., Nofal, T. A. (2020). Sawi decomposition method for Volterra integral equation with application. Journal of Mathematics, 2020, 1–13.
  • Aggarwal, S., Sharma, N., Chauhan, R. (2018). Solution of linear Volterra integral equations of second kind using Mohand transform. International Journal of Research in Advent Technology, 6(11), 3098–3102.
  • Ali, A. I., Kalim, M., Khan, A. (2022). Solutions of Volterra integral equations (VIEs) of the second kind with Bulge function using Aboodh transform. Scientific Inquiry and Review, 6(2), 21–31.
  • Sattaso, S., Nonlaopon, K., Kim, H. (2019). Further properties of Laplace-typed integral transforms. Dynamic Systems and Applications, 28, 195–215.
  • Kim, H. (2017). The solution of Laguerre’s equation by using G-transform. International Journal of Applied Engineering Research, 12(24), 16083–16086.
  • Şener, S. Ş., Çelik, E., Özdemir, E. (2021). The solution of linear Volterra integral equation of the first kind with ZZ-transform. Turkish Journal of Sciences, 6(3), 127–133.
  • Song, Y., Kim, H. (2014). The solution of Volterra integral equation of the second kind by using the Elzaki transform. Applied Mathematical Sciences, 8(11), 525–530.
  • Gnanavel, M. G., Saranya, C., Viswanathan, A. (2019). Applications of linear Volterra integral equations of first kind by using Tarig transform. International Journal of Innovative Technology and Exploring Engineering, 8(10), 2278–3075.
  • Haarsa, P. (2017). On volterra integral equations of the first kind by using Elzaki transform. Far East Journal of Mathematical Sciences,102(9), 1857-1863.
  • Aggarwal, S., Bhatnagar, K., Dua, A. (2019). Dualities between Elzaki transform and some useful integral transforms. International Journal of Innovative Technology and Exploring Engineering, 8(12), 4312–4318.
  • Aggarwal, S., Sharma, N. (2019). Laplace transform for the solution of first kind linear Volterra integral equation. Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 16–23.
  • Mishra, R., Aggarwal, S., Chaudhary, L., Kumar, A. (2020). Relationship between Sumudu and some efficient integral transforms. International Journal of Innovative Technology and Exploring Engineering, 9(3), 153–159.
  • Singh, G. P., Aggarwal, S. (2019). Sawi transform for population growth and decay problems. International Journal of Latest Technology in Engineering, Management & Applied Science, 8(8), 157–162.
  • Tunç, C., Mohammed, S. A. (2017). On the stability and instability of functional Volterra-integro differentaial equation of first order. Bulletin of Mathematical Analysis and Applications, 9(1), 151-160.
  • Tunç, C., Tunç, O (2019). A note on the qualitative analysis of Volterra integro-differential equations. Journal of Taibah University for Science, 13(1), 490–496.
  • Kim, H. (2017). The intrinsic structure and properties of Laplace-typed integral transforms. Mathematical Problems in Engineering, vol. 2017.
  • Aggarwal, S., Gupta, A. R., Singh, D. P., Asthana, N., Kumar, N. (2018). 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.
  • Elzaki, T. M. (2012). On the new integral transform "Elzaki transform" fundamental properties investigations and applications. Global Journal of Mathematical Sciences: Theory and Practical, 4(1), 1–13.
  • Aggarwal, S., Sharma, S. D., Vyas, A. (2020). Sawi transform of Bessel’s functions with application for evaluating definite integrals. International Journal of Latest Technology in Engineering, Management & Applied Science, 9, 12–18.
  • Eltayeb, H., Kılıçman, A. (2010). On some applications of a new integral transform. International Journal of Mathematical Analysis, 4(3), 123–132.

Year 2025, Volume: 6 Issue: 1, 102 - 112, 29.05.2025

Adil Mısır , İslam Alsalih

https://doi.org/10.63716/guffd.1548492

Abstract

References

  • Linz, P. (1974). A simple approximation method for solving Volterra integro-differential equations of the first kind. IMA Journal of Applied Mathematics, 14(2), 211–215.
  • Çimen, E. (2018). A computational method for Volterra integro-diferentialequation. Erzincan Fen Bilimleri Enstitüsü Dergisi, 11(3), 347–352.
  • Ajileye, G., Amoo S.A. (2023). Numerical solution to Volterra integro-differential equations using collocation approximation. Mathematics and Computational Sciences, 4(1), 1–8.
  • Zhou, H., Wang, Q., (2019). The Nystrom method and convergence analysis for system of Fredholm integral equations. Fundamental Journal of Mathematics and Applications, 2(1), 28-32.
  • Zhou, H., Wang, Q., (2019). Two-Grid iterative method for a class of Fredholm functional integral equations based on the radial basis function interpolation. Fundamental Journal of Mathematics and Applications, 2(2), 117-122.
  • Dafemos, C. M. (1970). An abstract Volterra equation with applications to linear viscoelasticity. Journal of Differential Equations, 7(3), 554–569.
  • Levinson, N. (1960). A nonlinear Volterra equation arising in the theory of superfluidity. Journal of Mathematical Analysis and Applications, 1(1), 1–11.
  • Shilepsky, C. C. (1974). The asymptotic behavior of an integral equation with an application to Volterra’s population equation. Journal of Mathematical Analysis and Applications, 48(3), 764–779.
  • Swick, K. E. (1981). A nonlinear model for human population dynamics. SIAM Journal on Applied Mathematics, 40(2), 266–278.
  • Distefano, N. (1968). A Volterra integral equation in the stability of some linear hereditary phenomena. Journal of Mathematical Analysis and Applications, 23(2), 365–383.
  • Philip, J. R. (1966). Some integral equations in geometrical probability. Biometrika, 53(3–4), 365–374.
  • Feller, W. (1941). On the integral equation of renewal theory. The Annals of Mathematical Statics, 12(3), 243–267.
  • Wang, F. J. S. (1978). Asymptotic behavior of some deterministic epidemic models. SIAM Journal on Mathematical Analysis, 9(3), 529–534.
  • Lin, S. P. (1975). Damped vibration of a string. Journal of Fluid Mechanics, 72(4), 787–797.
  • Rogers, T. G., Lee, E. H. (1964). The cylinder problem in viscoelastic stress analysis. Quarterly of Applied Mathematics, 22(2), 117–131.
  • Goldsmith, P. L. (1967). The calculation of true particle size distributions from the sizes observed in a thin slice. British Journal of Applied Physics, 18(6), 813.
  • Raisinghania, M. D. (2007). Integral equations and boundary value problems. New Delhi. S. Chand Publishing.
  • Rahman, M. (2007). Integral Equations and Their Applications. Boston. WIT press.
  • Polyanin, P., Manzhirov, A. V. (2008). Handbook of Integral Equations. London: Chapman and Hall/CRC.
  • Wazwaz, A. M. (2011). Linear and nonlinear integral equations. Berlin. Springer.
  • Pipkin, A. C. (1991). A Course on Integral Equations. New York Berlin Heidelberg. Springer Science & Business Media, 9.
  • Bitsadze, A. V. (1995). Integral Equations of First Kind. Singapore. World Scientific, 7.
  • Hackbusch, W. (1995). Integral Equation Theory and Numerical Treatment. Basel. Birkhauser press.
  • Aggarwal, S., Gupta, A. R., Sharma, S. D. (2019). A new application of Shehu transform for handling Volterra integral equations of first kind. International Journal of Research in Advent Technology, 7(4), 439–445.
  • Aggarwal, S., Sharma, N., Chauhan, R. (2018). Application of Kamal transform for solving linear Volterra integral equations of first kind. International Journal of Research in Advent Technology, 6(8), 2081–2088.
  • Higazy, M., Aggarwal, S., Nofal, T. A. (2020). Sawi decomposition method for Volterra integral equation with application. Journal of Mathematics, 2020, 1–13.
  • Aggarwal, S., Sharma, N., Chauhan, R. (2018). Solution of linear Volterra integral equations of second kind using Mohand transform. International Journal of Research in Advent Technology, 6(11), 3098–3102.
  • Ali, A. I., Kalim, M., Khan, A. (2022). Solutions of Volterra integral equations (VIEs) of the second kind with Bulge function using Aboodh transform. Scientific Inquiry and Review, 6(2), 21–31.
  • Sattaso, S., Nonlaopon, K., Kim, H. (2019). Further properties of Laplace-typed integral transforms. Dynamic Systems and Applications, 28, 195–215.
  • Kim, H. (2017). The solution of Laguerre’s equation by using G-transform. International Journal of Applied Engineering Research, 12(24), 16083–16086.
  • Şener, S. Ş., Çelik, E., Özdemir, E. (2021). The solution of linear Volterra integral equation of the first kind with ZZ-transform. Turkish Journal of Sciences, 6(3), 127–133.
  • Song, Y., Kim, H. (2014). The solution of Volterra integral equation of the second kind by using the Elzaki transform. Applied Mathematical Sciences, 8(11), 525–530.
  • Gnanavel, M. G., Saranya, C., Viswanathan, A. (2019). Applications of linear Volterra integral equations of first kind by using Tarig transform. International Journal of Innovative Technology and Exploring Engineering, 8(10), 2278–3075.
  • Haarsa, P. (2017). On volterra integral equations of the first kind by using Elzaki transform. Far East Journal of Mathematical Sciences,102(9), 1857-1863.
  • Aggarwal, S., Bhatnagar, K., Dua, A. (2019). Dualities between Elzaki transform and some useful integral transforms. International Journal of Innovative Technology and Exploring Engineering, 8(12), 4312–4318.
  • Aggarwal, S., Sharma, N. (2019). Laplace transform for the solution of first kind linear Volterra integral equation. Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 16–23.
  • Mishra, R., Aggarwal, S., Chaudhary, L., Kumar, A. (2020). Relationship between Sumudu and some efficient integral transforms. International Journal of Innovative Technology and Exploring Engineering, 9(3), 153–159.
  • Singh, G. P., Aggarwal, S. (2019). Sawi transform for population growth and decay problems. International Journal of Latest Technology in Engineering, Management & Applied Science, 8(8), 157–162.
  • Tunç, C., Mohammed, S. A. (2017). On the stability and instability of functional Volterra-integro differentaial equation of first order. Bulletin of Mathematical Analysis and Applications, 9(1), 151-160.
  • Tunç, C., Tunç, O (2019). A note on the qualitative analysis of Volterra integro-differential equations. Journal of Taibah University for Science, 13(1), 490–496.
  • Kim, H. (2017). The intrinsic structure and properties of Laplace-typed integral transforms. Mathematical Problems in Engineering, vol. 2017.
  • Aggarwal, S., Gupta, A. R., Singh, D. P., Asthana, N., Kumar, N. (2018). 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.
  • Elzaki, T. M. (2012). On the new integral transform "Elzaki transform" fundamental properties investigations and applications. Global Journal of Mathematical Sciences: Theory and Practical, 4(1), 1–13.
  • Aggarwal, S., Sharma, S. D., Vyas, A. (2020). Sawi transform of Bessel’s functions with application for evaluating definite integrals. International Journal of Latest Technology in Engineering, Management & Applied Science, 9, 12–18.
  • Eltayeb, H., Kılıçman, A. (2010). On some applications of a new integral transform. International Journal of Mathematical Analysis, 4(3), 123–132.
There are 45 citations in total.

Details

Primary Language Turkish
Subjects Applied Mathematics (Other)
Journal Section Araştırma Makaleleri
Authors

Adil Mısır 0000-0002-4552-0769

İslam Alsalih 0000-0001-8922-2328

Publication Date May 29, 2025
Submission Date September 18, 2024
Acceptance Date April 7, 2025
Published in Issue Year 2025 Volume: 6 Issue: 1

Cite

APA Mısır, A., & Alsalih, İ. (2025). Volterra integral denklemlerinin ve Volterra integro-diferensiyel denklemlerinin G_r-dönüşümü kullanılarak çözümü. Gazi Üniversitesi Fen Fakültesi Dergisi, 6(1), 102-112. https://doi.org/10.63716/guffd.1548492
AMA Mısır A, Alsalih İ. Volterra integral denklemlerinin ve Volterra integro-diferensiyel denklemlerinin G_r-dönüşümü kullanılarak çözümü. GÜFFD. May 2025;6(1):102-112. doi:10.63716/guffd.1548492
Chicago Mısır, Adil, and İslam Alsalih. “Volterra Integral Denklemlerinin Ve Volterra Integro-Diferensiyel Denklemlerinin G_r-dönüşümü kullanılarak çözümü”. Gazi Üniversitesi Fen Fakültesi Dergisi 6, no. 1 (May 2025): 102-12. https://doi.org/10.63716/guffd.1548492.
EndNote Mısır A, Alsalih İ (May 1, 2025) Volterra integral denklemlerinin ve Volterra integro-diferensiyel denklemlerinin G_r-dönüşümü kullanılarak çözümü. Gazi Üniversitesi Fen Fakültesi Dergisi 6 1 102–112.
IEEE A. Mısır and İ. Alsalih, “Volterra integral denklemlerinin ve Volterra integro-diferensiyel denklemlerinin G_r-dönüşümü kullanılarak çözümü”, GÜFFD, vol. 6, no. 1, pp. 102–112, 2025, doi: 10.63716/guffd.1548492.
ISNAD Mısır, Adil - Alsalih, İslam. “Volterra Integral Denklemlerinin Ve Volterra Integro-Diferensiyel Denklemlerinin G_r-dönüşümü kullanılarak çözümü”. Gazi Üniversitesi Fen Fakültesi Dergisi 6/1 (May 2025), 102-112. https://doi.org/10.63716/guffd.1548492.
JAMA Mısır A, Alsalih İ. Volterra integral denklemlerinin ve Volterra integro-diferensiyel denklemlerinin G_r-dönüşümü kullanılarak çözümü. GÜFFD. 2025;6:102–112.
MLA Mısır, Adil and İslam Alsalih. “Volterra Integral Denklemlerinin Ve Volterra Integro-Diferensiyel Denklemlerinin G_r-dönüşümü kullanılarak çözümü”. Gazi Üniversitesi Fen Fakültesi Dergisi, vol. 6, no. 1, 2025, pp. 102-1, doi:10.63716/guffd.1548492.
Vancouver Mısır A, Alsalih İ. Volterra integral denklemlerinin ve Volterra integro-diferensiyel denklemlerinin G_r-dönüşümü kullanılarak çözümü. GÜFFD. 2025;6(1):102-1.