Aboodh transform

The Aboodh transform is a type of integral transform. Khalid Suliman Aboodh formulated it in 2013. ^{[1] [2] [3] [4]} It is defined as a set

${\displaystyle A=\{f(t):\ni M,a,b>0,|f(t)|<Me^{-vt}\}}$

${\displaystyle a\leq v\leq b}$

${\displaystyle A[f(t)]={\frac {1}{v}}\int _{0}^{\infty }f(t)e^{-vt}\,dt}$

The Aboodh transform has been used in fields such as the double, ^[5] triple, ^{[6] [7]} and quadruple Aboodh transforms, ^[8] fuzzy logic ^{[9] [10]} and fractional theory. ^[11] Patil compared it to the Laplace transform. ^{[12] [13]}

References

1. Murali, Ramdoss; Selvan, Arumugam Ponmana; Park, Choonkil; Lee, Jung Rye (2021-06-15). "Aboodh transform and the stability of second order linear differential equations". Advances in Difference Equations. 2021 (1): 296. doi: 10.1186/s13662-021-03451-4 . ISSN   1687-1847.
2. Ojo, Gbenga O.; Mahmudov, Nazim I. (January 2021). "Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order". Mathematics. 9 (2): 155. doi: 10.3390/math9020155 . ISSN   2227-7390.
3. Aboodh, Khalid Suliman (2013-04-01). "The new integral transform "Aboodh transform"". Global Journal of Pure and Applied Mathematics. 9 (1): 35–44.
4. Selvam, A.; Sabarinathan, S.; Pinelas, Sandra (2023-09-24). "The Aboodh Transform Techniques to Ulam Type Stability of Linear Delay Differential Equation" . International Journal of Applied and Computational Mathematics. 9 (5): 115. doi:10.1007/s40819-023-01577-5. hdl: 10773/39817 . ISSN   2199-5796. S2CID   262148893.
5. Ouideen, Yasmin; Al-Aati, Ali (2022). "On Double Aboodh-Shehu Transform and Its Properties with Applications". Albaydha University Journal (in Arabic). 4 (3). doi: 10.56807/buj.v4i03.331 . ISSN   2709-9695.
6. "Triple Aboodh Transform".^{[ dead link ]}
7. Raghavendran, P.; Gunasekar, Th; Balasundaram, H.; Santra, Sh S.; Majumder, D.; D. Baleanu, D. (2023). "Solving fractional integro-differential equations by Aboodh transform". Journal of Mathematics and Computer Science. 32 (3): 229–240. doi: 10.22436/jmcs.032.03.04 . Retrieved 2024-01-19.
8. "Quadrapole".^{[ dead link ]}
9. "Fuzzy Aboodh Transform".^{[ dead link ]}
10. "Fuzzy Aboodh".
11. Zi̇ane, Djelloul; Belgacem, Rachid; Bokhari̇, Ahmed (2022-06-30). "Local Fractional Aboodh Transform and its Applications to Solve Linear Local Fractional Differential Equations". Advances in the Theory of Nonlinear Analysis and Its Application. 6 (2): 217–228. doi:10.31197/atnaa.979506. ISSN   2587-2648.
12. Patil, Dinkar (2018-12-01). "Comparative Study of Laplace, Sumudu, Aboodh, Elzaki and Mahgoub Transforms and Applications in Boundary Value Problems". SSRN   4094218.
13. Awuya, Michael A.; Subasi, D. S. (2021). "Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel". Symmetry. 13 (11): 2055. Bibcode:2021Symm...13.2055A. doi: 10.3390/sym13112055 .