Araştırma Makalesi

Yıl 2024,
Cilt: 8 Sayı: 1, 18 - 24, 07.06.2024
### Öz

### Anahtar Kelimeler

### Kaynakça

Investigating solutions of differential equations has been an important issue for scientists.

Researchers around the world have talked about different methods to solve differential equations.

The type and order of the differential equation enable us to decide the method that we can choose

to find the solution of the equation. One of these methods is the integral transform, which is the

conversion of a real or complex valued function into another function by some algebraic

operations. Integral transforms are used to solve many problems in mathematics and engineering,

such as differential equations and integral equations. Therefore, new types of integral transforms

have been defined, and existing integral transforms have been improved. One of the solution

methods of many physical problems as well as initial and boundary value problems are integral

transforms. Integral transforms were introduced in the first half of the 19th century. The first

historically known integral transforms are Laplace and Fourier transforms. Over the time, other

transforms that are used in many fields have emerged. The aim of this article is to describe the

Mohand transform and to make applications of linear ordinary differential equations with

constant coefficients without any major mathematical calculations This integral transform

method is an alternative method to existing transforms such as Laplace transform and Kushare

transform. When recent studies in the literature are examined, it can be said that Mohand

transform is preferred because it is easy to apply.

Differential equation Integral transform Laplace and Fourier transform.

- [1] Katre, N.T. and Katre, R.T. (2021). A comparative study of Laplace and Kamal transforms, International Conference on Research Frontiers in Sciences (ICRFS 2021), Nagpur, India, 5 th- 6 th February 2021.
- [2] Fadhil, R.A and Alkfari, B.H.A. (2023). Convolution HY transform for second kind of linear Volterra integral equation, Al-Kadhum 2nd International Conference on Modern Applications of Information and Communication Technology, 29 March 2023, Volume 2591, Issue 1.
- [3] Mohmad, Z.S. and Sadikali, L.S. (2021). Sadik Transform, The generalization of All the transform Who’s kernal is Of Exponential Form With The Application In Differential Equation With Variable Coefficients, Turkish Journal of Computer and Mathematics, 3264-3272.
- [4] Rashdi, H.Z. (2022). Using Anuj Transform to Solve Ordinary Differential Equations with Variable Coefficients, Scientific Journal for the Faculty of Scientific-Sirte University, Vol. 2, No. 1, 38-42.
- [5] Aggarwal, S. and Gupta, A.R. (2019). Dualities between Mohand Transform and Some Useful Integral Transforms. International Journal of Recent Tecnology and Engineering, 8 (3), 843-847.
- [6] Sornkaew, P. and Phollamat, K. (2021). Solution of Partial Differential Equations by Using Mohand Transforms, Journal of Physics: Conference Series, Vol. 1850, Iss. 1.
- [7] Saadeh, R. Qazza, A. and Burqan, A. (2020). A New Integral Transform: Ara Transform and Its Properties and Applications. Symmetry, 12 (6), 925.
- [8] Kushare, S.R., Patil, D.P. and Takate, A.M. (2021). The New Integral Transform “KUSHARE Transform”, International Journal of Advances in Engineering and Management. 3 (9), 1589-1592.
- [9] Johansyah, M.D., Supriatna, A.K., Rusyaman E. and Saputra, J. (2022). Solving Differential Equations of Fractional Order Using Combined Adomian Decomposition Method with Kamal Integral Transformation, Mathematics and Statistics, 10 (1), 187-194.
- [10] Patil, D.P. (2021). Aboodh and Mahgoub Transform in Boundary Value Problems. Scientific Journal for of System of Ordinary Differential Equations. International Journal of Advanced Research in Science, Communication and Technology, 6 (1), 67-75.
- [11] Aggarwal, S., Chauhan, R. and Sharma, N. (2018). Application of Aboodh Transform for Solving Linear Volterra Integro-Differential Equations of Secon Kind. International Journal of Research in Advent Technology, 6 (6), 1186-1190.
- [12] Attaweel, M.E. and Almassry, H. (2020). On the Mohand Transform and Ordinary Differential Equations with Variable Coefficients. Al-Mukhtar Journal of Sciences, 35 (1), 1-6.
- [13] Dehinsilu, O.A., Odentunde, O.S., Usman, M.A., Ogunyinka, P.I., Taiwo, A.I. and Onaneye, A.A. (2020). Solutions of Linear Convection-Diffusion Problems with Constant Coefficients Using Mahgoub Transform Method. FUW Trends in Science and Technology Journal, 5 (3), 891-894.
- [14] Abbas, E.S., Kuffi, E.A. and Abdlrasol, L.B. (2022). General Solution of Telegraph Equation Using Aboodh Transform. Mathematical Statistician and Engineering Applications, 71 (2), 267-271.
- [15] Aggarwal, S., Kumar, R. and Chandel, J. (2023). Solution of Linear Volterra Integral Equation of Second Kind via Rishi Transform. Journal of Scientific Research, 15 (1), 11-119.
- [16] Kuffi, E. and Maktoof, S.F. (2021). “Emad-Falih Transform” a new integral transform. Journal of Interdisciplinary Mathematics, 24 (8), 2381-2390.
- [17] Gupta, R. (2020). On Novel Integral Transform: Rohit Transform and Its Application to Boundary Value Problems. ASIO Journal of Chemistry, Physics, Mathematics and Applied Sciences, 4 (1), 08-12.
- [18] Aggarwal, S. and Chaudhary, R. (2019). A Comparative Study of Mohand and Laplace Transforms. Journalof Emerging Technologies and Innovative Research, 6 (2), 230-240.
- [19] Mushtt, I.Z., and Kuffi, E.A. (2023) Sadik and Complex Sadik Integral Transforms of System of Ordinary Differential Equations, Iraqi Journal for Computer Science and Mathematics, 4 (1), 181-190.
- [20] Mohand, M. and Mahgoub, A. (2017). The new integral transform “Mohand Transform”. Advances in Theoretical and Applied Mathematics, 12 (2), 113-120.
- [21] Aggarwal, S. and Chauhan, R. (2019). A Comparative Study of Mohand and Aboodh Transforms. International Journal of Research in Advent Technology, 7 (1), 520-529.
- [22] Kumar, P.S., Saranya, C., Gnanavel, M.G. and Viswanathan, A. (2018). Applications of Mohand transform for solving linear Volterra integral equations of first kind. International Journal of Research in Advent Technology, 6 (10), 2786-2789.

Yıl 2024,
Cilt: 8 Sayı: 1, 18 - 24, 07.06.2024
### Öz

### Kaynakça

- [1] Katre, N.T. and Katre, R.T. (2021). A comparative study of Laplace and Kamal transforms, International Conference on Research Frontiers in Sciences (ICRFS 2021), Nagpur, India, 5 th- 6 th February 2021.
- [2] Fadhil, R.A and Alkfari, B.H.A. (2023). Convolution HY transform for second kind of linear Volterra integral equation, Al-Kadhum 2nd International Conference on Modern Applications of Information and Communication Technology, 29 March 2023, Volume 2591, Issue 1.
- [3] Mohmad, Z.S. and Sadikali, L.S. (2021). Sadik Transform, The generalization of All the transform Who’s kernal is Of Exponential Form With The Application In Differential Equation With Variable Coefficients, Turkish Journal of Computer and Mathematics, 3264-3272.
- [4] Rashdi, H.Z. (2022). Using Anuj Transform to Solve Ordinary Differential Equations with Variable Coefficients, Scientific Journal for the Faculty of Scientific-Sirte University, Vol. 2, No. 1, 38-42.
- [5] Aggarwal, S. and Gupta, A.R. (2019). Dualities between Mohand Transform and Some Useful Integral Transforms. International Journal of Recent Tecnology and Engineering, 8 (3), 843-847.
- [6] Sornkaew, P. and Phollamat, K. (2021). Solution of Partial Differential Equations by Using Mohand Transforms, Journal of Physics: Conference Series, Vol. 1850, Iss. 1.
- [7] Saadeh, R. Qazza, A. and Burqan, A. (2020). A New Integral Transform: Ara Transform and Its Properties and Applications. Symmetry, 12 (6), 925.
- [8] Kushare, S.R., Patil, D.P. and Takate, A.M. (2021). The New Integral Transform “KUSHARE Transform”, International Journal of Advances in Engineering and Management. 3 (9), 1589-1592.
- [9] Johansyah, M.D., Supriatna, A.K., Rusyaman E. and Saputra, J. (2022). Solving Differential Equations of Fractional Order Using Combined Adomian Decomposition Method with Kamal Integral Transformation, Mathematics and Statistics, 10 (1), 187-194.
- [10] Patil, D.P. (2021). Aboodh and Mahgoub Transform in Boundary Value Problems. Scientific Journal for of System of Ordinary Differential Equations. International Journal of Advanced Research in Science, Communication and Technology, 6 (1), 67-75.
- [11] Aggarwal, S., Chauhan, R. and Sharma, N. (2018). Application of Aboodh Transform for Solving Linear Volterra Integro-Differential Equations of Secon Kind. International Journal of Research in Advent Technology, 6 (6), 1186-1190.
- [12] Attaweel, M.E. and Almassry, H. (2020). On the Mohand Transform and Ordinary Differential Equations with Variable Coefficients. Al-Mukhtar Journal of Sciences, 35 (1), 1-6.
- [13] Dehinsilu, O.A., Odentunde, O.S., Usman, M.A., Ogunyinka, P.I., Taiwo, A.I. and Onaneye, A.A. (2020). Solutions of Linear Convection-Diffusion Problems with Constant Coefficients Using Mahgoub Transform Method. FUW Trends in Science and Technology Journal, 5 (3), 891-894.
- [14] Abbas, E.S., Kuffi, E.A. and Abdlrasol, L.B. (2022). General Solution of Telegraph Equation Using Aboodh Transform. Mathematical Statistician and Engineering Applications, 71 (2), 267-271.
- [15] Aggarwal, S., Kumar, R. and Chandel, J. (2023). Solution of Linear Volterra Integral Equation of Second Kind via Rishi Transform. Journal of Scientific Research, 15 (1), 11-119.
- [16] Kuffi, E. and Maktoof, S.F. (2021). “Emad-Falih Transform” a new integral transform. Journal of Interdisciplinary Mathematics, 24 (8), 2381-2390.
- [17] Gupta, R. (2020). On Novel Integral Transform: Rohit Transform and Its Application to Boundary Value Problems. ASIO Journal of Chemistry, Physics, Mathematics and Applied Sciences, 4 (1), 08-12.
- [18] Aggarwal, S. and Chaudhary, R. (2019). A Comparative Study of Mohand and Laplace Transforms. Journalof Emerging Technologies and Innovative Research, 6 (2), 230-240.
- [19] Mushtt, I.Z., and Kuffi, E.A. (2023) Sadik and Complex Sadik Integral Transforms of System of Ordinary Differential Equations, Iraqi Journal for Computer Science and Mathematics, 4 (1), 181-190.
- [20] Mohand, M. and Mahgoub, A. (2017). The new integral transform “Mohand Transform”. Advances in Theoretical and Applied Mathematics, 12 (2), 113-120.
- [21] Aggarwal, S. and Chauhan, R. (2019). A Comparative Study of Mohand and Aboodh Transforms. International Journal of Research in Advent Technology, 7 (1), 520-529.
- [22] Kumar, P.S., Saranya, C., Gnanavel, M.G. and Viswanathan, A. (2018). Applications of Mohand transform for solving linear Volterra integral equations of first kind. International Journal of Research in Advent Technology, 6 (10), 2786-2789.

Toplam 22 adet kaynakça vardır.

Birincil Dil | İngilizce |
---|---|

Konular | Uygulamalı Matematik (Diğer) |

Bölüm | Research Articles |

Yazarlar | |

Erken Görünüm Tarihi | 18 Nisan 2024 |

Yayımlanma Tarihi | 7 Haziran 2024 |

Yayımlandığı Sayı | Yıl 2024Cilt: 8 Sayı: 1 |