Moazzam, A., Kuffi, E., Abideen, Z., Anjum, A. (2023). Two parametric SEE transformation and its applications in solving differential equations. Alustath, 16(2), 116-120. doi: 10.30772/qjes.v16i2.891
Ali Moazzam; Emad A. Kuffi; Zain Ul Abideen; Ayza Anjum. "Two parametric SEE transformation and its applications in solving differential equations". Alustath, 16, 2, 2023, 116-120. doi: 10.30772/qjes.v16i2.891
Moazzam, A., Kuffi, E., Abideen, Z., Anjum, A. (2023). 'Two parametric SEE transformation and its applications in solving differential equations', Alustath, 16(2), pp. 116-120. doi: 10.30772/qjes.v16i2.891
Moazzam, A., Kuffi, E., Abideen, Z., Anjum, A. Two parametric SEE transformation and its applications in solving differential equations. Alustath, 2023; 16(2): 116-120. doi: 10.30772/qjes.v16i2.891

Two parametric SEE transformation and its applications in solving differential equations

Al-Qadisiyah Journal for Engineering Sciences
Volume 16, Issue 2, June 2023, Pages 116-120    PDF (301.8 K)
Document Type: Research Paper
DOI: 10.30772/qjes.v16i2.891
Authors
Ali Moazzam* 1; Emad A. Kuffi2; Zain Ul Abideen3; Ayza Anjum3
1Department of Mathematics and Statistics, University of Agriculture, Jail Road Faisalabad, Pakistan
2Department of Material Engineering, College of Engineering, Al-Qadisiyah University, Iraq
3Department of Physics, University of Agriculture, Jail Road Faisalabad, Pakistan
Abstract
Transformation plays a much more important role in every science. In this research article, two parametric forms of SEE transformation have been explored and the fundamental properties of two parametric SEE transformations have been shown. Furthermore, the transformed function of some fundamental functions and their time derivative rule has been shown. The application of two parametric SEE transformations in solving differential equations has been shown. The radioactive decay problem in first-order linear differential equations has been solved in this article which has large applications in nuclear energy engineering. Further, the solution to the beam deflection problem has been shown to have many applications in the engineering field. These results can be compared with other Laplace-type transformations.
Keywords
Two Parametric; Differential Equations; Time Derivative; Beam Deflection; Radioactive Decay
References
  • Bildi, M. Inc, A comparison between Adomian decomposition and Tau methods, Abstract and Applied Analysis, 201(3) (2013) 183-197.
  • M. Wazwaz, The combined Kamal transform–Adomian decomposition method for handling nonlinear Volterra integro–differential equations, Appl. Math. Comp., 216(4) (2010) 1304–1309.
  • T. Rashed, Lagrange interpolation to compute the numerical solutions of differential, integral and differential-integro equations, Appl. Math. Comput., 151(3) (2004) 869–878.
  • Avudainayagam, C. Vani, Wavelet–Galerkin method for integro–differential equations, Appl. Numer. Math., 32(3) (2000) 247–254.
  • M. Wazwaz, A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations, Appl. Math. Comput., 181(2) (2006) 1703–1712.
  • A. Khuri, A Kamal decomposition algorithm applied to a class of nonlinear differential equations, J. Appl. Math., 1(4) (2001) 141–155.
  • Khan, M. Hussain, H. Jafari, Y. Khan, Application of Kamal decomposition method to solve nonlinear coupled partial differential equations, World Appl. Sci. J., 9(1) (2010) 13–19.
  • S. Elgazery, Numerical solution for the Falkner–Skan equation, Chaos Solitons Fractals, 35(4) (2008) 738–746.
  • Islam, Y. Khan, N. Faraz, F. Austin, Numerical solution of logistic differential equations by using the Kamal decomposition method, World Appl. Sci. J., 8(9) (2010) 1100–1105.
  • Yang, J. Hou, An Approximate Solution of Nonlinear Fractional Differential Equation by Kamal Transform and Adomian Polynomials, Journal of Information and computation, 27(1) (2013) 11-19.
  • J. Evans, K.R. Raslan, The Adomian decomposition method for solving delay differential equation, Int. J. Comput. Math., 82(1) (2005) 49–54.
  • M. Heris, Solving the Differential-integro Equations Using the Modified Kamal Adomian Decomposition Method, J. Math. Ext., 6 (2012).
  • A. Mohamed, M.S. Torky, Numerical solution of nonlinear system of partial differential equations by the Kamal decomposition method and the Pade approximation, Am. J. Comput. Math., 3(3) (2013) 175-184.
  • B. Yindoula, P. Youssouf, G. Bissanga, F. Bassono, B. Some, Application of the Adomian decomposition method and Kamal transform method to solving the convection diffusion-dissipation equation, Int. J. Appl. Math. Res., 3(1) (2014) 30-39.
  • A. Hamoud, K. P. Ghadle, The combined modified Kamal with Adomian decomposition method for solving the nonlinear Volterra-Fredholm integro differential equations, J. Korean Soc. Ind. Appl. Math., 21(1) (2017) 17–28.
  • Aggarwal, G.P. Singh GP, Aboodh transform of error function, Univ. Rev., 10(6) (2019) 137–150.
  • Aggarwal, S.D. Sharma, Sumudu transform of error function, J. Appl. Sci. Comput., 6(6) (2019) 1222–1231.
  • Aggarwal, A.R. Gupta, A. Kumar, Elzaki transform of error function, Glob. J. Eng. Sci. Res., 6(5) (2019) 412–422.
  • Aggarwal, A.R. Gupta, D. Kumar, Mohand transform of error function, Int. J. Res. Advent. Technol., 7(5) (2019) 224–231.
  • Aggarwal, S.D. Sharma, Application of Kamal transform for solving Abel’s integral equation, Glob. J. Eng. Sci. Res., 6(3) (2019) 82–90.
  • Aggarwal, G.P. Singh, Kamal transform of error function, J. Appl. Sci. Comput., 6(5) (2019) 2223–2235.
  • Mubarak, M.Z. Iqbal, A. Moazzam, U. Amjed, M.U. Naeem, Subtituition Method Using The Laplace Transformation For Solving Partial Differential Equations Involving More Than Two Independent Variables, Bulletin of Mathematics and Statistics Research, 9(3) (2021) 104-116.
  • I. Khawar, K. Shehzad, M.M.U. Rehman, Maria, A. Moazzam, Influence of Bio-convection and Activation Energy on Maxwell Flow of Nano-Fluid in the Existence of Motile Microorganisms over A Cylinder, International Journal of Multidisciplinary Research and Growth Evaluation, 2(5) (2021) 135-144.
  • Ayoub, M. Ghamkhar, A. Arif, A. Moazzam, Laplace Transforms Techniques on Equation of Advection-Diffussion in one-Dimensional With Semi-Infinite Medium to Find the Analytical Solution, Bulletin of Mathematics and Statistics Research, 9(3) (2021) 86-96.
  • Kashif, K. Shehzad, A. Moazzam, A. Ayoub, M. Bibi, New Transformation ‘AMK transformation’ to Solve Ordinary Linear Differential Equation of Moment Pareto Distribution, International Journal of Multidisciplinary Research and Growth Evaluation, 2(5) (2021) 125-134.
  • Moazzam, M. Kashif, U. Amjed, M.I. Khawar, Devolpment of A New Transformation to Solve a New Type of Ordinary Linear Differential Equation, Bulletin of Mathematics and Statistics Research, 9(3) (2021) 56-60.
  • Waqas, K. Shehzad, A. Moazzam, A. Batool, Applications of Kamal Transformation in Temperature Problems, Sch. J. Eng. Tech., 10(2) (2022) 5-8.
  • Eman, Mansour, E.A. Kuffi, A. Sadiq, Mehdi, on the SEE transform and system of ordinary differential equations, periodicals of engineering and natural sciences, 9(3) (2021) 277-281.
  • Moazzam, M.Z. Iqbal, Al-Zughair Transformations on Linear Differential Equations of Moment Pareto Distribution, Proc. 19th International Conference On Statistical Science, 36 (2022) 199-206.
  • Moazzam, M. Z. Iqbal, A New Integral Transform "Ali And Zafar" Transformation and It's Application in Nuclear Physics, Proc. 19th International Conference On Statistical Sciences, 36 (2022) 177-182.
 S. Aggarwal, A.R. Gupta, D. Singh, N. Asthana, N. Kumar, Application of Laplace   transform for solving population growth and decay problems. 

Statistics
Article View: 309
PDF Download: 191


Journal Management System. Powered by ejournalplus.com