In mathematics, the Natural transform is an
integral transform
In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than i ...
similar to the Laplace transform and Sumudu transform, introduced by Zafar Hayat Khan
in 2008. It converges to both Laplace and Sumudu transform just by changing variables. Given the convergence to the Laplace and Sumudu transforms, the N-transform inherits all the applied aspects of the both transforms. Most recently, F. B. M. Belgacem
has renamed it the natural transform and has proposed a detail theory and applications.
Formal definition
The natural transform of a
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-orie ...
''f''(''t''), defined for all real numbers ''t'' ≥ ''0'', is the function ''R''(''u'', ''s''), defined by:
:
Khan
showed that the above integral converges to
Laplace transform
In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the ''time domain'') to a function of a complex variable s (in the ...
when ''u'' = 1, and into
Sumudu transform for ''s'' = 1.
See also
*
References
Integral transforms
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