Research Article
Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations
Abstract
In this study, solutions of random complex partial differential equations were found using the two-dimensional Sumudu transformation method(STM). The initial conditions of a deterministic equation or the non-homogeneous part of the equation are transformed into random variables to obtain a random complex partial differential equation. With the help of the properties of two-dimensional Sumudu and inverse Sumudu transformation, an approximate analytical solution of a complex partial differential equation with random constant coefficients was obtained by selecting a random variable with an initial condition of Normal and Gamma distribution. The probability characteristics of the resulting solutions, such as expected value and variance, were obtained and graphically shown with the help of the Maple package program.
Keywords
Two-dimensional Sumudu and Inverse Sumudu Transformation Complex Differential Equation Expected Value Variance and Confidence Interval.
References
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Year 2024,
Volume: 45 Issue: 3, 562 - 570, 30.09.2024
Abstract
References
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- [4] Düz M., Solution of complex equations with Adomian Decomposition method, TWMS J. App. Eng. Math.,7(1) (2017) 66–73.
- [5] Watugala G. K., Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Int. J. Math. Educ. Sci. Technol., 24(1) (1993) 35–43.
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- [7] Weerakoon S., Application of Sumudu transform to partial differential equations, Int. J. Math. Educ. Sci. Technol., 25(2) (1994) 277–283.
- [8] Weerakoon S., Complex inversion formula for Sumudu transform, Int. J. Math. Educ. Sci. Technol. 29(4) (1998) 618–621.
- [9] Demiray S.T., Bulut H., Belgacem F.B.M., Sumudu transform method for analytical solutions of fractional type ordinary differential equations, Math Prob Eng., (2015) https ://doi.org/10.1155/2015/13169 0
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- [11] Rahman N.A.A., Ahmad M.Z., Solving fuzzy fractional differential equations using fuzzy Sumudu transform, J. Nonl. Sci. Appl., 10(5) (2017) 2620–2632
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- [13] Soong, T.T., Random Differential Equations in Science and Engineering, Academic Press, 327, (1973).
- [14] Belgacem F.B.M, Karaballi A.A, Sumudu Transform Fundamental Properties Investigations and Applications, J. Appl. Math. Stoch. Analy., (2006) Article ID 91083 1–23
- [15] Eltayeb H., Kılıçman A., A Note on the Sumudu Transforms and Differential Equations, Applied Math. Sci., 4(22) (2010) 1089 –1098.
- [16] Watugala, G.K. The Sumudu transform for functions of two variables, Mathematical Engin. in Indus., 8(4)(2002) 293–302.
- [17] Kılıçman A., Eltayeb H.,Agarwal R.P., On Sumudu Transform and System of Differential Equations, Abstract Appl. Analy., (2010), Article ID 598702, 11 pages.
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- [23] Merdan, M., Merdan, M., ve Şahin, R., Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method, Compl., (2023) 3713454.
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- [25] Musiela, M., Rutkowski, M., Martingale Methods in Financial Modelling, 2nd Edition, Springer Verlag, Berlin, (2004).
- [26] Øksendal, Bernt K., Stochastic Differential Equations: An Introduction with Applications. Berlin: Springer, (2003).
- [27] Kunita, H., Stochastic Differential Equations Based on Lévy Processes and Stochastic Flows of Diffeomorphisms. In: Rao, M.M. (eds) Real and Stochastic Analysis. Trends in Mathematics. Birkhäuser, (2004).
- [28] Imkeller P., Schmalfuss B., The Conjugacy of Stochastic and Random Differential Equations and the Existence of Global Attractors. J. Dyn. Diff. Equ., 13 (2) (2001) 215–249.
- [29] Michel E., Stochastic calculus in manifolds. Springer Berlin, Heidelberg, (1989).
- [30] Brzeźniak Z., Elworthy K.D., Stochastic differential equations on Banach manifolds, Methods Funct. Anal. Top. 6(1) (2000) 43-84.
- [31] Feller W., An Introduction to Probability Theory and Its Applications, volume 1, 3rd edition. New York: John Wiley & Sons. (1968)
- [32] Khaniyev, T., Ünver, İ., Küçük, Z., ve Kesemen T. (2017). Olasılık Kuramında Çözümlü Problemler, Nobel Akademik Yayıncılık.
There are 32 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | September 30, 2024 |
| Submission Date | February 27, 2023 |
| Acceptance Date | August 13, 2024 |
| Published in Issue | Year 2024Volume: 45 Issue: 3 |
