Properties and Application of Double Mohand Transform
Abstract
Differential equations are the convenient way to express several engineering and scientific problems, making it simple to identify their solutions. Different differential equations can be solved using a variety of analytical and numerical techniques. One of them is the integral transform technique. The fundamental properties of the double Mohand transform are derived, and the partial differential equations are used to illustrate how it might be applied. We also find the particular solutions to the partial differential equations in the current study. In comparison to other existing classical techniques for solving partial differential equations, the solution process and explanation demonstrate the flexible efficiency of the double Mohand transform. The outcome shows that the suggested approach is very effective, straightforward, and applicable to problems having partial differential equations.
References
1. Debnath L, Bhatta D. Integral transform and their application. 2nd ed. Chapman & Hall/CRC; 2016 Apr 19. p. 1-8.
2. Raisinghania MD. Advanced differential equations. S Chand & Co. Ltd; 2013 July 6. p. 1-54.
3. Jeffrey A. Advanced engineering mathematics. Harcourt Academic Press; 2002. p. 379-437.
4. Stroud KA, Booth DJ. Engineering mathematics. Industrial Press Inc.; 2001. p. 47-263.
5. Watugala GK. Sumudu transform: a new integral transform to solve differential equation and control engineering problems. Integr Educ. 1993 Jan 1;24(1):35-43.
6. Aggarwal S, Sharma SD. Sumudu transform of error function. J Appl Sci Comput. 2019 Jun;6(6):1222-31.
7. Elzaki TM. The new integral transform Elzaki Transform. Glob J Pure Appl Math. 2011 Jan 1;7(1):57-64.
8. Hassan MA, Elzaki TM. Double Elzaki transform decomposition method for solving non-linear partial differential equations. J Appl Math Phys. 2020 Aug 5;8:1463-71.
9. Ahmed S, Elzaki TM. On the comparative study integro-differential equations using difference numerical methods. J King Saud Univ Sci. 2020 Jan 1;32:84-9.
10. Aggarwal S, Chauhan R, Sharma N. Application of Elzaki transform for solving linear Volterra integral equations of first kind. Int J Res Advent Technol. 2018 Aug;6(12):3687-92.
11. Aboodh KS. The new integral transform ‘Aboodh Transform.’ Glob J Pure Appl Math. 2013 Apr 1;9(1):35-43.
12. Murali R, Selvan AP, Park C, Lee JR. Aboodh transform and the stability of second order linear differential equations. Adv Differ Equ. 2021 Jun 15;2021(1):296.
13. Ojo GO, Mahmudov NI. Aboodh Transform iterative method for spatial diffusion of a biological population with fractional-order. Mathematics. 2021 Jan;9(2):155.
14. Aggarwal S, Sharma N, Chauhan R. Application of Aboodh transform for solving linear Volterra integro-differential equations of second kind. Int J Res Advent Technol. 2018;7(3):156-8.
15. Kashuri A, Fundo A. A new integral transform. Adv Theor Appl Math. 2013 Jan;8(1):27-43.
16. Mohand M, Mahgoub A. The new integral transform Mohand Transform. Adv Theor Appl Math. 2017;12(2):113-20.
17. Patra A, Baliarsingh P, Dutta H. Solution to fractional evolution equation using Mohand transform. Math Comput Simul. 2022 Oct 1;200:557-70.
18. Khandelwal R, Khandelwal Y. Solution of Blasius equation concerning with Mohand transform. Int J Appl Comput Math. 2020 Oct;6(5):128.
19. Aggarwal S, Chaudhary R. A comparative study of Mohand and Laplace transforms. J Emerg Technol Innov Res. 2019 Feb;6(2):230-40.
20. Kamal A, Sedeeg H. The new integral transform Kamal Transform. Adv Theor Appl Math. 2016;11(4):451-8.
21. Aruldass AR, Pachaiyappan D, Park C. Kamal transform and ULAM stability of differential equations. J Appl Anal Comput. 2021 Jun 15;11(3):1631-9.
22. Samar CP, Saxena H. Solution of generalized fractional kinetic equation by Laplace and Kamal transformation. Int J Math Trend Technol. 2021;67(6):38-43.
23. Aggarwal S, Chauhan R, Sharma, N. A new application of Kamal transform for solving linear Volterra integral equations. Int J Latest Technol Eng Manag Appl Sci. 2018;6(8):2081-8.
24. Kilicman A, Gadain HE. An application of double Laplace transforms and Sumudu transform. Lobachevskii J Math. 2009 Jul;30(3):214-23.
25. Jadhav S, Basotia V, Hiwarekar A. An application of double Elzaki transform in partial differential equations. Int J Adv Res Sci Commun Technol. 2022;2(1):181-6.
26. Aboodh KS, Farah RA, Almardy IA, Almostafa FA. Solution of telegraph equation by using double Aboodh transform. Elixir Appl Math. 2017 Sep 19;110:48213-7.
27. Patil DP. Solution of wave equation by double Laplace and double Sumudu transform. Vidyabharti Int Res J. 2021 Aug 1;(Sp Iss):135-8.
2. Raisinghania MD. Advanced differential equations. S Chand & Co. Ltd; 2013 July 6. p. 1-54.
3. Jeffrey A. Advanced engineering mathematics. Harcourt Academic Press; 2002. p. 379-437.
4. Stroud KA, Booth DJ. Engineering mathematics. Industrial Press Inc.; 2001. p. 47-263.
5. Watugala GK. Sumudu transform: a new integral transform to solve differential equation and control engineering problems. Integr Educ. 1993 Jan 1;24(1):35-43.
6. Aggarwal S, Sharma SD. Sumudu transform of error function. J Appl Sci Comput. 2019 Jun;6(6):1222-31.
7. Elzaki TM. The new integral transform Elzaki Transform. Glob J Pure Appl Math. 2011 Jan 1;7(1):57-64.
8. Hassan MA, Elzaki TM. Double Elzaki transform decomposition method for solving non-linear partial differential equations. J Appl Math Phys. 2020 Aug 5;8:1463-71.
9. Ahmed S, Elzaki TM. On the comparative study integro-differential equations using difference numerical methods. J King Saud Univ Sci. 2020 Jan 1;32:84-9.
10. Aggarwal S, Chauhan R, Sharma N. Application of Elzaki transform for solving linear Volterra integral equations of first kind. Int J Res Advent Technol. 2018 Aug;6(12):3687-92.
11. Aboodh KS. The new integral transform ‘Aboodh Transform.’ Glob J Pure Appl Math. 2013 Apr 1;9(1):35-43.
12. Murali R, Selvan AP, Park C, Lee JR. Aboodh transform and the stability of second order linear differential equations. Adv Differ Equ. 2021 Jun 15;2021(1):296.
13. Ojo GO, Mahmudov NI. Aboodh Transform iterative method for spatial diffusion of a biological population with fractional-order. Mathematics. 2021 Jan;9(2):155.
14. Aggarwal S, Sharma N, Chauhan R. Application of Aboodh transform for solving linear Volterra integro-differential equations of second kind. Int J Res Advent Technol. 2018;7(3):156-8.
15. Kashuri A, Fundo A. A new integral transform. Adv Theor Appl Math. 2013 Jan;8(1):27-43.
16. Mohand M, Mahgoub A. The new integral transform Mohand Transform. Adv Theor Appl Math. 2017;12(2):113-20.
17. Patra A, Baliarsingh P, Dutta H. Solution to fractional evolution equation using Mohand transform. Math Comput Simul. 2022 Oct 1;200:557-70.
18. Khandelwal R, Khandelwal Y. Solution of Blasius equation concerning with Mohand transform. Int J Appl Comput Math. 2020 Oct;6(5):128.
19. Aggarwal S, Chaudhary R. A comparative study of Mohand and Laplace transforms. J Emerg Technol Innov Res. 2019 Feb;6(2):230-40.
20. Kamal A, Sedeeg H. The new integral transform Kamal Transform. Adv Theor Appl Math. 2016;11(4):451-8.
21. Aruldass AR, Pachaiyappan D, Park C. Kamal transform and ULAM stability of differential equations. J Appl Anal Comput. 2021 Jun 15;11(3):1631-9.
22. Samar CP, Saxena H. Solution of generalized fractional kinetic equation by Laplace and Kamal transformation. Int J Math Trend Technol. 2021;67(6):38-43.
23. Aggarwal S, Chauhan R, Sharma, N. A new application of Kamal transform for solving linear Volterra integral equations. Int J Latest Technol Eng Manag Appl Sci. 2018;6(8):2081-8.
24. Kilicman A, Gadain HE. An application of double Laplace transforms and Sumudu transform. Lobachevskii J Math. 2009 Jul;30(3):214-23.
25. Jadhav S, Basotia V, Hiwarekar A. An application of double Elzaki transform in partial differential equations. Int J Adv Res Sci Commun Technol. 2022;2(1):181-6.
26. Aboodh KS, Farah RA, Almardy IA, Almostafa FA. Solution of telegraph equation by using double Aboodh transform. Elixir Appl Math. 2017 Sep 19;110:48213-7.
27. Patil DP. Solution of wave equation by double Laplace and double Sumudu transform. Vidyabharti Int Res J. 2021 Aug 1;(Sp Iss):135-8.
Published
2024-09-23
How to Cite
ULLAH, Shakir; AGGARWAL, Sudhanshu.
Properties and Application of Double Mohand Transform.
Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 9, n. 3&4, p. 1-12, sep. 2024.
ISSN 2455-7021.
Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/1286>. Date accessed: 21 dec. 2024.
Section
Research Article
