Aboodh transform

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Short description: An integral 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

[math]\displaystyle{ A = \{ f(t) : \ni M , a , b \gt 0 ,|f(t) | \lt M e^{-vt}\} }[/math]
[math]\displaystyle{ a \leq v \le b }[/math]
[math]\displaystyle{ A [f(t)]= \frac {1}{v} \int_0^\infty f(t) e^{- vt} \, dt }[/math]

The Aboodh transform has been used in fields such as the double,[5] triple,[6][7][8] and quadruple Aboodh transforms,[9] fuzzy logic[10][11][12] and fractional theory.[13] Patil compared it to the Laplace transform.[14][15][16]

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" (in en). Mathematics 9 (2): 155. doi:10.3390/math9020155. ISSN 2227-7390. 
  3. ↑ Aboodh, Khalid Suliman (2013-04-01). "The new integral transform "Aboodh transform"" (in English). Global Journal of Pure and Applied Mathematics 9 (1): 35–44. https://go.gale.com/ps/i.do?p=AONE&sw=w&issn=09731768&v=2.1&it=r&id=GALE%7CA331488712&sid=googleScholar&linkaccess=abs. 
  4. ↑ Selvam, A.; Sabarinathan, S.; Pinelas, Sandra (2023-09-24). "The Aboodh Transform Techniques to Ulam Type Stability of Linear Delay Differential Equation" (in en). International Journal of Applied and Computational Mathematics 9 (5): 115. doi:10.1007/s40819-023-01577-5. ISSN 2199-5796. https://doi.org/10.1007/s40819-023-01577-5. 
  5. ↑ Ouideen, Yasmin; Al-Aati, Ali (2022). "On Double Aboodh-Shehu Transform and Its Properties with Applications" (in ar). Albaydha University Journal 4 (3). doi:10.56807/buj.v4i03.331. ISSN 2709-9695. https://baydaauniv.net/buj/index.php/buj/article/view/331. 
  6. ↑ Alfaqeih, T. Özis S. (2019). "Note on Triple Aboodh Transform and Its Application" (in en). IJEAIS 3 (3): 1–7. https://philarchive.org/rec/SALNOT-3. 
  7. ↑ "Triple Aboodh Transform". https://ijarsct.co.in/Paper1361.pdf&sa=U&ved=2ahUKEwj37vynxuiDAxUCZmwGHQCWBpg4HhAWegQIBRAC&usg=AOvVaw0oT0p6BuW-SHG1hcDrRdqY. [|permanent dead link|dead link}}]
  8. ↑ Raghavendran, P.; Gunasekar, Th; Balasundaram, H.; Santra, Sh S.; Majumder, D.; D. Baleanu, D. (2023). "Solving fractional integro-differential equations by Aboodh transform" (in en). Journal of Mathematics and Computer Science 32 (3): 229–240. doi:10.22436/jmcs.032.03.04. https://www.isr-publications.com/jmcs/articles-12773-solving-fractional-integro-differential-equations-by-aboodh-transform. Retrieved 2024-01-19. 
  9. ↑ "Quadrapole". https://www.naturalspublishing.com/download.asp%3FArtcID%3D19889&sa=U&ved=2ahUKEwiG7ueNyeiDAxUkcmwGHXD5BtY4MhAWegQIAhAC&usg=AOvVaw0DD65uy67dGjdkjIHv3b_m. [|permanent dead link|dead link}}]
  10. ↑ "Fuzzy Aboodh Transform". https://ijnaa.semnan.ac.ir/article_5942.html&sa=U&ved=2ahUKEwie6MGGyuiDAxW2UGwGHUJKDzg4PBAWegQIBBAC&usg=AOvVaw1oIcY0RGHG2PhhDQCKDwxJ. [|permanent dead link|dead link}}]
  11. ↑ "Fuzzy Aboodh". https://philstat.org/index.php/MSEA/article/download/85/80&sa=U&ved=2ahUKEwja57_AyOiDAxWyTmwGHRqpBE84KBAWegQIAhAC&usg=AOvVaw1RA1UuZG73V5BudTrOgmmx. 
  12. ↑ Oyewumi, A. A.; Oderinu, R. A. (2022-09-01). "Application of the Combined Aboodh and Reduced Differential Transform Methods to the Fisher's Type Equations" (in en). Asian Journal of Pure and Applied Mathematics 4 (1): 572–585. https://globalpresshub.com/index.php/AJPAM/article/view/1659. 
  13. ↑ Zi̇ane, Djelloul; Belgacem, Rachid; Bokhari̇, Ahmed (2022-06-30). "Local Fractional Aboodh Transform and its Applications to Solve Linear Local Fractional Differential Equations" (in en). Advances in the Theory of Nonlinear Analysis and Its Application 6 (2): 217–228. doi:10.31197/atnaa.979506. ISSN 2587-2648. https://dergipark.org.tr/en/pub/atnaa/issue/68040/979506. 
  14. ↑ Patil, Dinkar (2018-12-01) (in en), Comparative Study of Laplace, Sumudu, Aboodh, Elzaki and Mahgoub Transforms and Applications in Boundary Value Problems, Rochester, NY, https://papers.ssrn.com/abstract=4094218, retrieved 2024-01-19 
  15. ↑ Awuya, Michael A.; Subasi, D. S. (2021). "Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel" (in en). Symmetry 13 (11): 2055. doi:10.3390/sym13112055. Bibcode: 2021Symm...13.2055A. 
  16. ↑ Ojo, Gbenga O.; Mahmudov, Nazim I. (2021-04-20). "Application of Aboodh Transform Iterative Method for Solving Time – Fractional Partial Differential Equations" (in en). International Journal of Sciences: Basic and Applied Research (IJSBAR) 57 (2): 65–85. ISSN 2307-4531. https://www.gssrr.org/index.php/JournalOfBasicAndApplied/article/view/12424. 



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