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

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

a\leq v\leq b

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

^ 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.
^ 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.
^ Aboodh, Khalid Suliman (2013-04-01). "The new integral transform "Aboodh transform"". Global Journal of Pure and Applied Mathematics. 9 (1): 35–44.
^ 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.
^ 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.
^ "Triple Aboodh Transform".^{[dead link]}
^ 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.
^ "Quadrapole".^{[dead link]}
^ "Fuzzy Aboodh Transform".^{[dead link]}
^ "Fuzzy Aboodh".
^ 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.
^ Patil, Dinkar (2018-12-01). "Comparative Study of Laplace, Sumudu, Aboodh, Elzaki and Mahgoub Transforms and Applications in Boundary Value Problems". SSRN 4094218.
^ 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.

[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.

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