Abstract
In this paper, we introduce a new type of integral transforms, called the ARA integral transform that is defined as: G n [ g ( t ) ] ( s ) = G ( n , s ) = s ∫ 0 ∞ t n − 1 e − s t g ( t ) d t , s > 0 . We prove some properties of ARA transform and give some examples. Also, some applications of the ARA transform are given.
Highlights
The integral transforms play a vital role in finding solutions to initial value problems and initial boundary value problems
In this paper, we introduce a new type of integral transforms, called the ARA integral transform that is defined as: Gn [ g(t)](s) = G(n, s) = s tn−1 e−st g(t)dt, s > 0
We prove some properties of ARA transform and give some examples
Summary
The integral transforms play a vital role in finding solutions to initial value problems and initial boundary value problems. An integral transform T [1] has the form. The integral transform was introduced by the French mathematician and physicist P.S. Laplace [2,3]. Fourier [4] introduced the Fourier transform. Mathematicians have been interested in developing and establishing new integral transforms. In 1993, Watugula [5] introduced the Sumudu transform. The natural transform was introduced by Khan and Khan [6] in 2008. In the year 2017, other transforms were introduced, Symmetry 2020, 12, 925; doi:10.3390/sym12060925 www.mdpi.com/journal/symmetry.
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