APPLICATION OF KHARRAT-TOMA TRANSFORM FOR SOLVING LINEAR VOLTERRA INTEGRAL EQUATIONS

Öz

In this paper, a new integral transform, called Kharrat-Toma transform is used for solving convolution type linear Volterra integral equations of the rst kind and also convolution type linear Volterra integral equation of the second kind. Some applications are given to explain the procedure of solution of linear Volterra integral equations using Kharrat-Toma transform.

Anahtar Kelimeler

• Integral equations
• Integral transforms
• Kharrat-Toma transform
• Volterra integral equations

Kaynakça

1. 1: H. A. Abdallah and A. M. Shama, Applications of differential transform method to integral equations, Amer. J. Engg. Res. (AJER), vol.7(1), pp.71-276 (2018).
2. 2 : S. Aggarwal, R. Chauhan and N. Sharma, Application of Aboodh transform for solving linear Volterra integro-differential equations of second kind, Int. J. Res. Adv. Tech., vol.6(8), pp. 1186-1190 (2018).
3. 3 : S. Aggarwal, R. Chauhan and N. Sharma, A new application of Kamal transform for solving linear Volterra integral equations, Int. J. Lat. Tech. Engg., Magn. &App. Sci., vol.7(4), pp.138-140 (2018).
4. 4 : S. Aggarwal, R. Chauhan and N. Sharma, Application of Kamal transform for solving linear Volterra integral equations of first kind, Int. J. Res. Adv. Tech., vol.6(8), pp.2081-2088 (2018).
5. 5 : S. Aggarwal, R. Chauhan and N. Sharma, A new application of Mahgoub transform for solving linear Volterra integral equations, Asi. Res., Vol.7(2), pp. 46-48 (2018).
6. 6 : S. Aggarwal, R. Chauhan and N. Sharma, A New Application of Shehu Transform for Handling Volterra Integral Equations of First Kind, International Journal of Research in Advent Technology, Vol.7(4), pp.439-445 (2019).
7. 7 : M. A. Asiru, Sumudu Transform and the Solution of Integral Equations of Convolution Type, International Journal of Mathematical Education in Science and Technology, vol.32(6), pp.906-910 (2001).
8. 8 : M.G. Gnanavel, C. Saranya and A. Viswanathan, Applications of Linear Volterra Integral Equations of First Kind by Using Tarig Transform, International Journal of Innovative Technology and Exploring Engineering (IJITEE), Vol.8(10), pp.2278-3075 (2019).

9. 9 : P. Haarsa, On Volterra integral equations of the first kind by using Elzaki transform," Far East J. Mat. Sci. (FJMS), vol. 102(9), pp.1857-1863 (2017).
10. 10 : B.N.Kharrat and G.A.Toma, A New Integral Transform:Kharrat-Toma Transform and Its Properties, World Applied Sciences Journal, vol.38(5), pp.436-443 (2020).
11. 11 : M. Rahman, Integral Equations and Their Applications, WIT press, Boston, (2007).
12. 12 : P. Senthil Kumar, M. G. Gnanavel and V. Viswanathan, Application of Mohand Tranform for Solving Linear Volterra Integro -- Differential Equations", Int. J. Res. Adv. Tech., vol. 6(10), pp. 2554-2556 (2018).
13. 13 : P. Senthil Kumar, C. Saranya, M. G. Gnanavel and A. Viswanathan, Application of Mohand Tranform for Solving Linear Volterra Integral Equations of First Kind, Int. J. Res. Adv. Tech., vol. 6(10), pp. 2786-2789 (2018).
14. 14 : Y. Song and H. Kim, The Solution of Volterra Integral Equation of the Second Kind by Using the Elzaki Transform, Applied Mathematical Sciences, Vol.8(11), pp.525-530 (2014).
15. 15 : V. Volterra, Theory of functional of integral and integro-differential equations, Dover, New York, (1959).
16. 16 : A. M. Wazwaz, A first course in integral equations. World Scientific, Second Edition, Singapore, (2015).
17. 17 : A. M. Wazwaz, Linear and Nonlinear Integral Equations Methods and Applications, Springer Verlag Berlin Heidelberg, (2011).