Department of Mathematics, University of Mazandaran, Babolsar, Iran.
Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa.
J Adv Res. 2020 Aug 28;32:133-138. doi: 10.1016/j.jare.2020.08.016. eCollection 2021 Sep.
Integral transforms are important to solve real problems. Appropriate choice of integral transforms helps to convert differential equations as well as integral equations into terms of an algebraic equation that can be solved easily.During last two decades many integral transforms in the class of Laplace transform are introduced such as Sumudu, Elzaki, Natural, Aboodh, Pourreza, Mohand, G_transform, Sawi and Kamal transforms.
In this paper, we introduce a general integral transform in the class of Laplace transform. 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 and G_transforms, Pourreza, Aboodh and etc.
A new integral transform is introduced. Then some properties of this integral transform are discussed. This integral transform is used to solve this new transform is used for solving higher order initial value problems, integral equations and fractional order integral equation.
It is proved that those new transforms in the class of Laplace transform which are introduced during last few decades are a special case of this general transform. It is shown that there is no advantage between theses transforms unless for special problems.
It has shown that this new integral transform covers those exiting transforms such as Laplace, Elzaki and Sumudu transforms for different value of () and (). We used this new transform for solving ODE, integral equations and fractional integral equations. Also, we can introduce new integral transforms by using this new general integral transform.
积分变换对于解决实际问题非常重要。适当选择积分变换有助于将微分方程和积分方程转换为易于求解的代数方程。在过去的二十年中，已经引入了许多属于拉普拉斯变换类的积分变换，如 Sumudu、Elzaki、Natural、Aboodh、Pourreza、Mohand、G_transform、Sawi 和 Kamal 变换。
在本文中，我们引入了拉普拉斯变换类中的一种通用积分变换。我们研究了这个变换的性质，然后将其与拉普拉斯家族中的一些现有积分变换，如 Laplace、Sumudu、Elzaki 和 G_transform、Pourreza、Aboodh 等进行了比较。
引入了一种新的积分变换，然后讨论了这个积分变换的一些性质。这个积分变换用于求解这个新的变换可以用于求解高阶初值问题、积分方程和分数阶积分方程。
证明了过去几十年中引入的拉普拉斯变换类中的那些新变换是这个通用变换的特例。除非对于特殊问题，否则这些变换之间没有优势。
表明这个新的积分变换涵盖了那些现有的变换，如 Laplace、Elzaki 和 Sumudu 变换，对于不同的值（）和（）。我们使用这个新的变换来求解 ODE、积分方程和分数阶积分方程。此外，我们还可以通过使用这个新的通用积分变换来引入新的积分变换。
