Application of Kashuri Fundo Transform to Decay Problem

Abstract

Recently, it has become quite common to investigate the solutions of
problems that have an important place in scientific fields by using integral
transforms. The most important reason for this is that this transform allows the
simplest and least number of calculations to be made while reaching the solutions
of the problems. In this study, we are looking for a solution to the decay problem,
which has a very important place in fields such as economics, chemistry, zoology,
biology and physics, by using the Kashuri Fundo transform, which is one of the
integral transforms. In order to reveal the ease of use of this transform in reaching
the solution, some numerical applications were examined. The results of these
numerical applications reveal that the Kashuri Fundo transform is quite efficient in
reaching the solution of the decay problem.

Keywords

• Integral transform
• Kashuri Fundo transform
• Inverse Kashuri Fundo transform
• Decay problem

Kashuri Fundo Dönüşümünün Bozunma Problemine Uygulanması

Abstract

Son zamanlarda, bilimsel alanlarda önemli bir yere sahip olan problemlerin çözümlerinin integral dönüşümleri kullanılarak araştırılması oldukça yaygın hale
gelmiştir. Bunun en önemli nedeni, bu dönüşümün problemlerin çözümüne ulaşırken en basit ve en az sayıda hesaplamanın yapılmasına olanak sağlamasıdır.
Bu çalışmada ekonomi, kimya, zooloji, biyoloji ve fizik gibi alanlarda çok önemli bir yere sahip olan bozunma problemine integral dönüşümlerden biri olan Kashuri
Fundo dönüşümü kullanılarak çözüm aranmaktadır. Çözüme ulaşmada bu dönüşümün kullanım kolaylığını ortaya koymak için bazı sayısal uygulamalar
incelenmiştir. Bu sayısal uygulamaların sonuçları, Kashuri Fundo dönüşümünün bozunma probleminin çözümüne ulaşmada oldukça verimli olduğunu ortaya
koymaktadır.

Keywords

• İntegral dönüşümü
• Kashuri Fundo dönüşümü
• Ters Kashuri Fundo dönüşümü
• Bozunma problemi

References

1. [1] Bronson, R., Costa, G. B. 2006. Schaum’s Outline of Differential Equations. 3rd, McGraw-Hill, 408s.
2. [2] Gorain, G. C. 2014. Introductory Course on Differential Equations. Alpha Science International, Narosa, 598s.
3. [3] Kapur, J. N. 2005. Mathematical Modelling. 2nd, New-Age International Pvt Ltd Publishers.
4. [4] Aggarwal, S., Asthana, N., Singh, D. P. 2018. Solution of Population Growth and Decay Problems by Using Aboodh Transform Method. International Journal of Research in Advent Technology, 6(10), 2706-2710.
5. [5] Aggarwal, S., Gupta, A. R., Asthana, N., Singh, D. P. 2018. Application of Kamal Transform for Solving Population Growth and Decay Problems. Global Journal of Engineering Science and Researches, 5(9), 254-260.
6. [6] 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.
7. [7] Aggarwal, S., Pandey, M., Asthana, N., Singh, D. P., Kumar, N. 2018. Application of Mahgoub Transform for Solving Population Growth and Decay Problems. Journal of Computer and Mathematical Sciences, 9(10), 1490-1496.
8. [8] Aggarwal, S., Sharma, N., Chauhan, R. 2018. Solution of Population Growth and Decay Problems by Using Mohand Transform. International Journal of Research in Advent Technology, 6(11), 3277-3282.

9. [9] Aggarwal, S., Singh, D. P., Asthana, N., Gupta, A. R. 2018. Application of Elzaki Transform for Solving Population Growth and Decay Problems. Journal of Emerging Technologies and Innovative Research, 5(9), 281-284.
10. [10]Aggarwal, S., Sharma, S. D., Gupta, A. R. 2019.Application of Shehu Transform for HandlingGrowth and Decay Problems. Global Journal ofEngineering Science and Researches, 6(4), 190-198.
11. [11]Aggarwal, S., Sharma, S. D., Kumar, N., Vyas, A.2020. Solutions of Population Growth and DecayProblems Using Sumudu Transform. International Journal of Research and Innovation in Applied Science, 5(7), 2454-6194.
12. [12]Rao, R. U. 2017. ZZ Transform Method forNatural Growth and Decay Problems.International Journal of Progressive Sciencesand Technologies, 5(2), 147-150.
13. [13]Mansour, E. A., Kuffi, E. A., Mehdi, S. A. 2021.Solving Population Growth and Decay ProblemsUsing Complex SEE Transform. 7th InternationalConference on Contemporary InformationTechnology and Mathematics, 18-19 August2021, Mosul, 243-246.
14. [14]Singh, G. P., Aggarwal, S. 2019. Sawi Transformfor Population Growth and Decay Problems.International Journal of Latest Technology inEngineering, Management & Applied Science,8(8), 157-162.
15. [15]Kashuri, A., Fundo, A. 2013. A New IntegralTransform. Advances in Theoretical and AppliedMathematics, 8(1), 27-43.
16. [16]Kashuri, A., Fundo, A., Liko, R. 2013. On DoubleNew Integral Transform and Double LaplaceTransform. European Scientific Journal, 9(33),82-90.
17. [17]Kashuri, A., Fundo, A., Liko, R. 2015. NewIntegral Transform For Solving Some FractionalDifferential Equations. International Journal ofPure and Applied Mathematics, 103(4), 675-682.
18. [18]Helmi, N., Kiftiah, M., Prihandono, B. 2016.Penyelesaian Persamaan Diferensial ParsialLinear Dengan Menggunakan MetodeTransformasi Artıon-Fundo. Buletin IlmiahMatematika, Statistika dan Terapannya, 5(3),195-204.
19. [19]Dhange, N. D. 2020. A New Integral Transformand Its Applications in Electric Circuits andMechanics. Journal of Emerging Technologiesand Innovative Research, 7(11), 80-86.
20. [20]Güngör, N. 2021. Solving Convolution TypeLinear Volterra Integral Equations with KashuriFundo Transform. Journal of Abstract andComputational Mathematics, 6(2), 1-7.
21. [21]Cuha, F. A., Peker, H. A. 2022. Solution of Abel’sIntegral Equation by Kashuri Fundo Transform.Thermal Science, 26(4A), 3003-3010.
22. [22]Peker, H. A., Cuha, F. A., Peker, B. 2022. SolvingSteady Heat Transfer Problems via KashuriFundo Transform. Thermal Science, 26(4A),3011-3017.
23. [23]Kashuri, A., Fundo, A., Kreku, M. 2013. Mixture ofa New Integral Transform and HomotopyPerturbation Method for Solving NonlinearPartial Differential Equations. Advances in PureMathematics, 3(3), 317-323.
24. [24]Shah, K., Singh, T. 2015. A Solution of theBurger’s Equation Arising in the LongitudinalDispersion Phenomenon in Fluid Flow throughPorous Media by Mixture of New IntegralTransform and Homotopy Perturbation Method.Journal of Geoscience and EnvironmentProtection, 3(4), 24-30.
25. [25]Shah, K., Singh, T. 2015. The Mixture of NewIntegral Transform and Homotopy PerturbationMethod for Solving Discontinued ProblemsArising in Nanotechnology. Open Journal ofApplied Sciences, 5(11), 688-695.
26. [26]Subartini, B., Sumiati, I., Sukono, Riaman,Sulaiman, I. M. 2021. Combined AdomianDecomposition Method with Integral Transform.Mathematics and Statistics, 9(6), 976-983.
27. [27]Peker, H. A., Cuha, F. A. 2022. Application ofKashuri Fundo Transform and HomotopyPerturbation Methods to Fractional HeatTransfer and Porous Media Equations. ThermalScience, 26(4A), 2877-2884.
28. [28]Johansyah, M. D., Supriatna, A. K., Rusyaman, E.,Saputra, J. 2022. Solving the Economic GrowthAcceleration Model with Memory Effects: AnApplication of Combined Theorem of AdomianDecomposition Methods and Kashuri–FundoTransformation Methods. Symmetry, 14(2),192, https://doi.org/10.3390/sym14020192.