Abstract
In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. This method is generalized in the sense of conformable derivative. Important results and theorems concerning this method are discussed. A new algorithm is proposed to solve linear and nonlinear partial differential equations in three dimensions. Moreover, some examples are provided to verify the performance of the proposed algorithm. This method presents a wide applicability to solve nonlinear partial differential equations in the sense of conformable derivative.
Highlights
Fractional calculus has attracted many researchers in the last decades. e impact of this fractional calculus on both pure and applied branches of science and engineering has been increased
While conformable derivative has been criticized in [3, 4], we believe that the new definition deserves to be explored further with its analysis and applications because many research studies have been conducted on this definition and its applications to various phenomena in physics and engineering. erefore, throughout this paper, we will call this definition as conformable derivative
We prove the basic eorem 1 and the relation between the conformable partial fractional derivatives (CPFDs) and partial derivatives as follows
Summary
Fractional calculus has attracted many researchers in the last decades. e impact of this fractional calculus on both pure and applied branches of science and engineering has been increased. We refer to [4, 18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35] that many researchers have been worked on different analogues methods to solve partial fractional differential in conformable sense. A combined method of both of the Laplace transform and resolvent kernel methods was introduced in [31] Motivated by all these studies, we come up with the idea to study the nonlinear partial fractional differential equations by defining a function in 3-dimensional space. Erefore, a conformable triple Laplace transform is defined and coupled with Adomian decomposition method to solve systematic nonlinear partial fractional differential equations.
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