Aboodh transform

The Aboodh transform is a type of integral transform. Khalid Suliman Aboodh formulated it in 2013.<ref>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.</ref><ref>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.</ref><ref>Aboodh, Khalid Suliman (2013-04-01). "The new integral transform "Aboodh transform"". Global Journal of Pure and Applied Mathematics. 9 (1): 35–44.</ref><ref>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. ISSN 2199-5796. S2CID 262148893.</ref> It is defined as a set

<math>A = \{ f(t) : \ni M , a , b > 0 ,|f(t) | < M e^{-vt}\} </math>

<math>a \leq v \le b </math>

<math> 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,<ref>Ouideen, Yasmin; Al-Aati, Ali (2022). "On Double Aboodh-Shehu Transform and Its Properties with Applications". Albaydha University Journal (in العربية). 4 (3). doi:10.56807/buj.v4i03.331. ISSN 2709-9695.</ref> triple,<ref>Alfaqeih, T. Özis S. (2019). "Note on Triple Aboodh Transform and Its Application". IJEAIS. 3 (3): 1–7.</ref><ref>"Triple Aboodh Transform".</ref><ref>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.</ref> and quadruple Aboodh transforms,<ref>"Quadrapole".</ref> fuzzy logic<ref>"Fuzzy Aboodh Transform".</ref><ref>"Fuzzy Aboodh".</ref><ref>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". Asian Journal of Pure and Applied Mathematics. 4 (1): 572–585.</ref> and fractional theory.<ref>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.</ref> Patil compared it to the Laplace transform.<ref>Patil, Dinkar (2018-12-01), Comparative Study of Laplace, Sumudu, Aboodh, Elzaki and Mahgoub Transforms and Applications in Boundary Value Problems (SSRN Scholarly Paper), Rochester, NY, SSRN 4094218, retrieved 2024-01-19{{citation}}: CS1 maint: location missing publisher (link)</ref><ref>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.</ref><ref>Ojo, Gbenga O.; Mahmudov, Nazim I. (2021-04-20). "Application of Aboodh Transform Iterative Method for Solving Time – Fractional Partial Differential Equations". International Journal of Sciences: Basic and Applied Research (IJSBAR). 57 (2): 65–85. ISSN 2307-4531.</ref>