TY - JOUR T1 - Volterra integral denklemlerinin ve Volterra integro-diferensiyel denklemlerinin G_r-dönüşümü kullanılarak çözümü AU - Mısır, Adil AU - Alsalih, İslam PY - 2025 DA - May Y2 - 2025 DO - 10.63716/guffd.1548492 JF - Gazi Üniversitesi Fen Fakültesi Dergisi JO - GÜFFD PB - Gazi Üniversitesi WT - DergiPark SN - 2757-5543 SP - 102 EP - 112 VL - 6 IS - 1 LA - tr AB - 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. KW - Volterra integral denklemleri KW - Volterra integro-differensiyel denklemleri KW - G_r-dönüşümü CR - 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. CR - Çimen, E. (2018). A computational method for Volterra integro-diferentialequation. Erzincan Fen Bilimleri Enstitüsü Dergisi, 11(3), 347–352. CR - Ajileye, G., Amoo S.A. (2023). Numerical solution to Volterra integro-differential equations using collocation approximation. Mathematics and Computational Sciences, 4(1), 1–8. CR - 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. CR - 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. CR - Dafemos, C. M. (1970). An abstract Volterra equation with applications to linear viscoelasticity. Journal of Differential Equations, 7(3), 554–569. CR - Levinson, N. (1960). A nonlinear Volterra equation arising in the theory of superfluidity. Journal of Mathematical Analysis and Applications, 1(1), 1–11. CR - 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. CR - Swick, K. E. (1981). A nonlinear model for human population dynamics. SIAM Journal on Applied Mathematics, 40(2), 266–278. CR - 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. CR - Philip, J. R. (1966). Some integral equations in geometrical probability. Biometrika, 53(3–4), 365–374. CR - Feller, W. (1941). On the integral equation of renewal theory. The Annals of Mathematical Statics, 12(3), 243–267. CR - Wang, F. J. S. (1978). Asymptotic behavior of some deterministic epidemic models. SIAM Journal on Mathematical Analysis, 9(3), 529–534. CR - Lin, S. P. (1975). Damped vibration of a string. Journal of Fluid Mechanics, 72(4), 787–797. CR - Rogers, T. G., Lee, E. H. (1964). The cylinder problem in viscoelastic stress analysis. Quarterly of Applied Mathematics, 22(2), 117–131. CR - 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. CR - Raisinghania, M. D. (2007). Integral equations and boundary value problems. New Delhi. S. Chand Publishing. CR - Rahman, M. (2007). Integral Equations and Their Applications. Boston. WIT press. CR - Polyanin, P., Manzhirov, A. V. (2008). Handbook of Integral Equations. London: Chapman and Hall/CRC. CR - Wazwaz, A. M. (2011). Linear and nonlinear integral equations. Berlin. Springer. CR - Pipkin, A. C. (1991). A Course on Integral Equations. New York Berlin Heidelberg. Springer Science & Business Media, 9. CR - Bitsadze, A. V. (1995). Integral Equations of First Kind. Singapore. World Scientific, 7. CR - Hackbusch, W. (1995). Integral Equation Theory and Numerical Treatment. Basel. Birkhauser press. CR - 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. CR - 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. CR - Higazy, M., Aggarwal, S., Nofal, T. A. (2020). Sawi decomposition method for Volterra integral equation with application. Journal of Mathematics, 2020, 1–13. CR - 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. CR - 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. CR - Sattaso, S., Nonlaopon, K., Kim, H. (2019). Further properties of Laplace-typed integral transforms. Dynamic Systems and Applications, 28, 195–215. CR - Kim, H. (2017). The solution of Laguerre’s equation by using G-transform. International Journal of Applied Engineering Research, 12(24), 16083–16086. CR - 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. CR - 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. CR - 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. CR - 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. CR - 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. CR - 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. CR - 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. CR - 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. CR - 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. CR - 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. CR - Kim, H. (2017). The intrinsic structure and properties of Laplace-typed integral transforms. Mathematical Problems in Engineering, vol. 2017. CR - 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. CR - 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. CR - 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. CR - Eltayeb, H., Kılıçman, A. (2010). On some applications of a new integral transform. International Journal of Mathematical Analysis, 4(3), 123–132. UR - https://doi.org/10.63716/guffd.1548492 L1 - https://dergipark.org.tr/tr/download/article-file/4207338 ER -