From Wikipedia, the free encyclopedia
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
A
=
{
f
(
t
)
:∋
M
,
a
,
b
>
0
,
|
f
(
t
)
|
<
M
e
−
v
t
}
{\displaystyle A=\{f(t):\ni M,a,b>0,|f(t)|<Me^{-vt}\}}
a
≤
v
≤
b
{\displaystyle a\leq v\leq b}
A
f
(
t
)
=
1
v
∫
0
∞
f
(
t
)
e
−
v
t
d
t
{\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
^ 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 .