| Autor: |
Ibrahim, Israa A., Taha, Wafaa M., Alobaidi, Mizal, Jameel, Ali F., Bashier, Eihab, Alshirawi, Nawal H. |
| Předmět: |
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| Zdroj: |
Mathematical Modelling of Engineering Problems; Jan2024, Vol. 11 Issue 1, p185-191, 7p |
| Abstrakt: |
The fundamental purpose of this investigation is to make use of an analytical approach in order to solve and assess initial boundary value problems that are in the form of fractional partial differential equations (FPDEs). Intricate scientific phenomena that are marked by hereditary characteristics that are passed down from one generation to the next can be better understood with the help of the FPDEs, which are extremely useful instruments. In particular, when working with non-linear equations, it can be difficult to obtain analytical solutions that are either exact or approximate for these equations. In order to address these obstacles, the homogeneous balancing method (HBM) is being investigated in great detail and expanded in an innovative way in order to solve nonlinear physical problems that include FPDEs. HBM is renowned for its capacity for solving both linear and nonlinear fractional models, employing a direct approach that utilises a closed-form solution. The present study introduces an expanded version of the HBM that integrates the ideas of fractional calculus, specifically focusing on fractional derivative techniques. The approach is illustrated by analytically solving and examining two types of nonlinear FPDEs: the space-time fractional-coupled Burger's equation and the conformable fractional version of the Gerdjikov-Lvanov equations (GL), which encompass hyperbolic, trigonometric, and rational solutions. The efficiency of the extended form of the HBM is demonstrated by analyzing and comparing the acquired results with those reported in the literature. HBM would make a significant contribution towards overcoming the obstacles of existing methods, such that the proposed method will help us simplify the complexity of the nonlocal derivative when solving FPDEs. Overall, this work presents a feasible and efficient analytical approach for solving nonlinear FPDE using an extension form of the HD method with result analysis. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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