Numerical Inversion of Laplace Transform via Wavelet Operational Matrix and Its Applications to Fractional Differential Equations

Aruldoss, R.; Balaji, K.

doi:10.1007/s40819-021-01222-z

Cited by 4 publications

(1 citation statement)

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“…Using an appropriate integral transform helps to reduce differential and integral operators, from a considered domain into multiplication operators in another domain. Solving the deduced problem in the new domain, and then applying the inverse transform serve to invert the manipulated solution back to the required solution of the problem in its original domain (see, [1][2][3][4][5][6][7][8][9][10][11][12][13]). The classical integral transforms used in solving differential equations, integral equations, and in analysis and the theory of functions are the Laplace transform, the Fourier integral transform .…”

Section: Introductionmentioning

confidence: 99%

The New Integral Transform: “NE Transform” and Its Applications

Xhaferraj

2023

European Journal of Formal Sciences and Engineering

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This work introduces a new integral transform for functions of exponential order called “NE integral transform”. We prove some properties of NE -transform. Also, some applications of the NE- transform to find the solution to ordinary linear equation are given. The relationships of the new transform with well-known transforms are characterized by integral identities. We study the properties of this transform. Then we compare it with few exiting integral transforms in the Laplace family such as Laplace, Sumudu, Elzaki, Aboodh and etc. As well, the NE integral transform is applied and used to find the solution of linear ordinary differential equations.

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