BEYOND SUMUDU TRANSFORM AND NATURAL TRANSFORM: $ {\mathbb J} $-TRANSFORM PROPERTIES AND APPLICATIONS

Weidong Zhao; Shehu Maitama

doi:10.11948/20180258

2020 Volume 10 Issue 4

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Weidong Zhao, Shehu Maitama. BEYOND SUMUDU TRANSFORM AND NATURAL TRANSFORM: $ {\mathbb J} $-TRANSFORM PROPERTIES AND APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1223-1241. doi: 10.11948/20180258

Citation:

Weidong Zhao, Shehu Maitama. BEYOND SUMUDU TRANSFORM AND NATURAL TRANSFORM: $ {\mathbb J} $-TRANSFORM PROPERTIES AND APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1223-1241. doi: 10.11948/20180258

BEYOND SUMUDU TRANSFORM AND NATURAL TRANSFORM: $ {\mathbb J} $-TRANSFORM PROPERTIES AND APPLICATIONS

Weidong Zhao¹,
Shehu Maitama^1, ,

1.
School of Mathematics, Shandong University, Jinan, Shandong, China

Corresponding author: Email address: smusman12@sci.just.edu.jo (S.Maitama)
Fund Project: This research is partially supported by National Natural Science Foundations of China (11571206). The first author also acknowledges the financial support of China Scholarship Council (CSC) (2017GXZ025381)

Abstract

Abstract

In this paper, we introduce an efficient integral transform called the $ {\mathbb J} $-transform which is a modification of the well-known Sumudu transform and the Natural transform for solving differential equations with real applications in applied physical sciences and engineering. The $ {\mathbb J} $-transform is more advantageous than both the Sumudu transform and the Natural transform. Interestingly, our proposed $ {\mathbb J} $-transform can be applied successfully to solve complex problems that are ordinarily beyond the scope of either Sumudu transform or Natural transform. As a proof of concept, we consider some classic examples and highlight the limitations of the previously reported integral transforms and lastly demonstrate the superiority of the proposed $ {\mathbb J} $-transform in addressing those limitations.
- Laplace transform /
- Sumudu transform /
- Natural transform /
- Elzaki transform /
- ordinary and partial differential equations.
MSC: 44A10, 44A15, 44A20, 44A30, 44A35

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References

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