Abstract
Recently, it was introduced a new integral transform viz. ZZ transform which generalizes the Laplace and Aboodh integral transforms. In this paper, we have addressed the relationship among the ZZ transform with Laplace and Aboodh transforms. Further, the ZZ transform is applied to the fractional derivative with Mittag-Leffler kernel defined in both the Caputo and Riemann-Liouville sense. In order to illustrate the validity and applicability of the transform, we have solved some illustrative examples.
Highlights
Specialty section: This article was submitted to Mathematical and Statistical Physics, a section of the journal Frontiers in Physics
We establish the relationship between the Zain Ul Abadin Zafar (ZZ) transform (ZZT) with the Aboodh transform (AT), and the Laplace transform (LT) having their various applications given in [27,28,29,30,31]
The organization of the paper is as follows: In section Preliminaries and Basic Definitions, we establish the connection between the Aboodh and ZZ transform; we prove some significant results and create the relationships between AB derivatives with ZZT
Summary
Fractional calculus (FC) has gained considerable achievements in various fields of science and engineering. In [13], a new fractional operator (AB) with a Mittag-Leffler kernel was developed In this regard, many researchers [14,15,16] have given their interest in this definition to solve various problems/models. We establish the relationship between the ZZ transform (ZZT) with the Aboodh transform (AT), and the Laplace transform (LT) having their various applications given in [27,28,29,30,31]. The ZZT has been applied to AB fractional operators defined in the Caputo and R-L sense, which are described in terms of theorems. The organization of the paper is as follows: In section Preliminaries and Basic Definitions, we establish the connection between the Aboodh and ZZ transform; we prove some significant results and create the relationships between AB derivatives with ZZT.
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