Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations

Mehmet Merdan; Merve Merdan; Rıdvan Şahin

doi:10.17776/csj.1256101

EN

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

[1] Düz M., Solution of complex differential equations with variable coefficients by using reduced differential transform, Mis. Math. Not., 21(1) (2020) 161–170.
[2] Düz M., Application of Elzaki Transform to first order constant coefficients complex equa ions, Bul. Int. math. Virt. inst., 7 (2017) 387–393.
[3] Düz M., On an application of Laplace transforms, NTMSCI., 5(2) (2017) 193–198.
[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.
[6] Anac H., Merdan M., Kesemen T., Solving for the random component time-fractional partial differential equations with the new Sumudu transform iterative method, SN App. Sci., 2 (2020) 1112 .
[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
[10] Kumar M., Daftardar-Gejji V., Exact solutions of fractional partial differential equations by Sumudu transform iterative method., (2018) arXiv :1806.03057 v1

[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
[12] Prakash A., Kumar M., Baleanu D., A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform, Appl. Math. Comput., 334 (2018) 30–40.
[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.
[18] Merdan M., Anac H., Bekiryazici Z., Kesemen, T., Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace-Padé Method, J. Gumushane Univ. Inst. Sci. Tech., 9(1) (2019) 108-118.
[19] Merdan M., Atasoy N., On Solutions Of Random Partial Differential Equations With Laplace Adomian Decomposition, Cumhuriyet Sci. J., 44(1) (2023) 160-169.
[20] Merdan M., Şişman Ş., Analysıs of Random Discrete Tıme Logistic Model, Sigma J. Eng. Nat. Sci., 38(3) (2020) 1269-1298.
[21] Merdan M., Altay Ö., Bekiryazici Z., Investigation of the Behaviour of Volterra Integral Equations with Random Effects, J. Gumushane Univ. Inst. Sci. Tech., 10(1) (2020) 205-216.
[22] Merdan M., Ordinary and partial complex differential equations with random effects. Master's Thesis, Gumushane University, Institute of Science, (2020).
[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.
[24] Rogers, L.C.G., Williams, David., Diffusions, Markov Processes and Martingales, Vol 2: Ito Calculus (2nd ed., Cambridge Mathematical Library ed.). Cambridge University Press.(2000).
[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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Mehmet Merdan ^*
0000-0002-8509-3044
Türkiye

Merve Merdan
0000-0002-6045-6531
Türkiye

Rıdvan Şahin
0000-0002-4597-7320
Türkiye

Publication Date

September 30, 2024

Submission Date

February 27, 2023

Acceptance Date

August 13, 2024

Published in Issue

Year 2024 Volume: 45 Number: 3

DOI

https://doi.org/10.17776/csj.1256101

IZ

https://izlik.org/JA67WG66KD

APA

Merdan, M., Merdan, M., & Şahin, R. (2024). Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations. Cumhuriyet Science Journal, 45(3), 562-570. https://doi.org/10.17776/csj.1256101

AMA

1.Merdan M, Merdan M, Şahin R. Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations. CSJ. 2024;45(3):562-570. doi:10.17776/csj.1256101

Chicago

Merdan, Mehmet, Merve Merdan, and Rıdvan Şahin. 2024. “Investigation of Solution Behavior of Differential Equations by Sumudu Methods of Random Complex Partial Differential Equations”. Cumhuriyet Science Journal 45 (3): 562-70. https://doi.org/10.17776/csj.1256101.

EndNote

Merdan M, Merdan M, Şahin R (September 1, 2024) Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations. Cumhuriyet Science Journal 45 3 562–570.

IEEE

[1]M. Merdan, M. Merdan, and R. Şahin, “Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations”, CSJ, vol. 45, no. 3, pp. 562–570, Sept. 2024, doi: 10.17776/csj.1256101.

ISNAD

Merdan, Mehmet - Merdan, Merve - Şahin, Rıdvan. “Investigation of Solution Behavior of Differential Equations by Sumudu Methods of Random Complex Partial Differential Equations”. Cumhuriyet Science Journal 45/3 (September 1, 2024): 562-570. https://doi.org/10.17776/csj.1256101.

JAMA

1.Merdan M, Merdan M, Şahin R. Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations. CSJ. 2024;45:562–570.

MLA

Merdan, Mehmet, et al. “Investigation of Solution Behavior of Differential Equations by Sumudu Methods of Random Complex Partial Differential Equations”. Cumhuriyet Science Journal, vol. 45, no. 3, Sept. 2024, pp. 562-70, doi:10.17776/csj.1256101.

Vancouver

1.Mehmet Merdan, Merve Merdan, Rıdvan Şahin. Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations. CSJ. 2024 Sep. 1;45(3):562-70. doi:10.17776/csj.1256101

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December

Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations

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