Aboodh transform

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The Aboodh transform is a type of integral transform. Khalid Suliman Aboodh formulated it in 2013.{{Cite journal |last1=Murali |first1=Ramdoss |last2=Selvan |first2=Arumugam Ponmana |last3=Park |first3=Choonkil |last4=Lee |first4=Jung Rye |date=2021-06-15 |title=Aboodh transform and the stability of second order linear differential equations |journal=Advances in Difference Equations |volume=2021 |issue=1 |pages=296 |doi=10.1186/s13662-021-03451-4 |doi-access=free |issn=1687-1847}}{{Cite journal |last1=Ojo |first1=Gbenga O. |last2=Mahmudov |first2=Nazim I. |date=January 2021 |title=Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order |journal=Mathematics |language=en |volume=9 |issue=2 |pages=155 |doi=10.3390/math9020155 |doi-access=free |issn=2227-7390}}{{Cite journal |last=Aboodh |first=Khalid Suliman |date=2013-04-01 |title=The new integral transform "Aboodh transform" |url=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 |journal=Global Journal of Pure and Applied Mathematics |language=English |volume=9 |issue=1 |pages=35–44}}{{Cite journal |last1=Selvam |first1=A. |last2=Sabarinathan |first2=S. |last3=Pinelas |first3=Sandra |date=2023-09-24 |title=The Aboodh Transform Techniques to Ulam Type Stability of Linear Delay Differential Equation |url=https://doi.org/10.1007/s40819-023-01577-5 |journal=International Journal of Applied and Computational Mathematics |language=en |volume=9 |issue=5 |pages=115 |doi=10.1007/s40819-023-01577-5 |s2cid=262148893 |issn=2199-5796|hdl=10773/39817 |hdl-access=free }} It is defined as a set

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

: $a \leq v \le b$

: $A [f(t)]= \frac {1}{v} \int_0^\infty f(t) e^{- vt} \, dt$

The Aboodh transform has been used in fields such as the double,{{Cite journal |last1=Ouideen |first1=Yasmin |last2=Al-Aati |first2=Ali |date=2022 |title=On Double Aboodh-Shehu Transform and Its Properties with Applications |url=https://baydaauniv.net/buj/index.php/buj/article/view/331 |journal=Albaydha University Journal |language=ar |volume=4 |issue=3 |doi=10.56807/buj.v4i03.331 |issn=2709-9695}} triple,{{Cite web |title=Triple Aboodh Transform |url=https://ijarsct.co.in/Paper1361.pdf&sa=U&ved=2ahUKEwj37vynxuiDAxUCZmwGHQCWBpg4HhAWegQIBRAC&usg=AOvVaw0oT0p6BuW-SHG1hcDrRdqY }}{{dead link|date=November 2023}}{{Cite journal |last1=Raghavendran |first1=P. |last2=Gunasekar |first2=Th |last3=Balasundaram |first3=H. |last4=Santra |first4=Sh S. |last5=Majumder |first5=D. |last6=D. Baleanu |first6=D. |title=Solving fractional integro-differential equations by Aboodh transform |url=https://www.isr-publications.com/jmcs/articles-12773-solving-fractional-integro-differential-equations-by-aboodh-transform |journal=Journal of Mathematics and Computer Science |date=2023 |language=en |volume=32 |issue=3 |pages=229–240 |doi=10.22436/jmcs.032.03.04 |access-date=2024-01-19 |doi-access=free }} and quadruple Aboodh transforms,{{Cite web |title=Quadrapole |url=https://www.naturalspublishing.com/download.asp%3FArtcID%3D19889&sa=U&ved=2ahUKEwiG7ueNyeiDAxUkcmwGHXD5BtY4MhAWegQIAhAC&usg=AOvVaw0DD65uy67dGjdkjIHv3b_m }}{{dead link|date=November 2023}} fuzzy logic{{Cite web |title=Fuzzy Aboodh Transform |url=https://ijnaa.semnan.ac.ir/article_5942.html&sa=U&ved=2ahUKEwie6MGGyuiDAxW2UGwGHUJKDzg4PBAWegQIBBAC&usg=AOvVaw1oIcY0RGHG2PhhDQCKDwxJ }}{{dead link|date=November 2023}}{{Cite web |title=Fuzzy Aboodh |url=https://philstat.org/index.php/MSEA/article/download/85/80&sa=U&ved=2ahUKEwja57_AyOiDAxWyTmwGHRqpBE84KBAWegQIAhAC&usg=AOvVaw1RA1UuZG73V5BudTrOgmmx}} and fractional theory.{{Cite journal |last1=Zi̇ane |first1=Djelloul |last2=Belgacem |first2=Rachid |last3=Bokhari̇ |first3=Ahmed |date=2022-06-30 |title=Local Fractional Aboodh Transform and its Applications to Solve Linear Local Fractional Differential Equations |url=https://dergipark.org.tr/en/pub/atnaa/issue/68040/979506 |journal=Advances in the Theory of Nonlinear Analysis and Its Application |language=en |volume=6 |issue=2 |pages=217–228 |doi=10.31197/atnaa.979506 |issn=2587-2648}} Patil compared it to the Laplace transform.{{cite SSRN |last=Patil |first=Dinkar |title=Comparative Study of Laplace, Sumudu, Aboodh, Elzaki and Mahgoub Transforms and Applications in Boundary Value Problems |date=2018-12-01 |ssrn=4094218}}{{Cite journal |last1=Awuya |first1=Michael A. |last2=Subasi |first2=D. S. |date=2021 |title=Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–Leffler Kernel |journal=Symmetry |language=en |volume=13 |issue=11 |page=2055 |doi=10.3390/sym13112055|doi-access=free |bibcode=2021Symm...13.2055A }}

References

Category:Integral transforms