Analysis on determining the solution of fourth-order fuzzy initial value problem with Laplace operator-Reference-Cited by-同舟云学术

Analysis on determining the solution of fourth-order fuzzy initial value problem with Laplace operator

Published:2022 Issue:12 Volume:19 Page:11868-11902
ISSN:1551-0018
Container-title:Mathematical Biosciences and Engineering
language:
Short-container-title:MBE

Author:

Akram Muhammad¹,Ihsan Tayyaba¹,Allahviranloo Tofigh²,Al-Shamiri Mohammed M. Ali³⁴

Affiliation:

1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

2. Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey

3. Department of Mathematics, Faculty of Science and Arts, Muhayl Asser, King Khalid University, K.S.A

4. Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen

Abstract

<abstract><p>This study presents a new analytical method to extract the fuzzy solution of the fuzzy initial value problem (FIVP) of fourth-order fuzzy ordinary differential equations (FODEs) using the Laplace operator under the strongly generalized Hukuhara differentiability (SGH-differentiability). To this end, firstly the fourth-order derivative of the fuzzy valued function (FVF) according to the type of the SGH-differentiability is introduced, and then the relationships between the fourth-order derivative of the FVF and its Laplace transform are established. Furthermore, considering the types of differentiabilities and switching points, some fundamental theorems related to the Laplace transform of the fourth-order derivative of the FVF are stated and proved in detail and a method to solve FIVP by the fuzzy Laplace transform is presented in detail. An application of our proposed method in Resistance-Inductance circuit (RL circuit) is presented. Finally, FIVP's solution is graphically analyzed to visualize and support theoretical results.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modeling and Simulation,General Medicine

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