Solution method for fifth-order fuzzy initial value problem

Muhammad Akram; Muhammad Yousuf; Muhammad Bilal

doi:10.1007/s41066-023-00403-z

Solution method for fifth-order fuzzy initial value problem

Muhammad Akram^*
, Muhammad Yousuf
, Muhammad Bilal

^*Corresponding author for this work

Research output: Contribution to journal › Review article › peer-review

2 Scopus citations

Abstract

Fuzzy differential equations (FDEs) are the general concept of ordinary differential equations. FDE seems to be a natural way to model the propagation of cognitive uncertainty in dynamic environments. This article establishes the characteristics of the strongly generalized Hukuhara differentiability (SGHD)-based fifth-order derivative of the fuzzy-valued function (FVF). The Laplace operator is used in SGHD to create a strategy for solving the fifth-order fuzzy initial value problem (FIVP). Furthermore, some examples of FIVP are addressed to exploit liability and the efficiency of our proposed method. Furthermore, the switching points and solutions of FIVP are presented graphically to demonstrate and corroborate the theoretical findings. Additionally, an application of a mass-spring-damper system is solved by our proposed method.

Original language	English
Pages (from-to)	1229-1252
Number of pages	24
Journal	Granular Computing
Volume	8
Issue number	6
DOIs	https://doi.org/10.1007/s41066-023-00403-z
State	Published - Nov 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Generalized Hukuhara differentiability
Initial-value problem
Mittag–Leffler function
Switching point

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Artificial Intelligence

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10.1007/s41066-023-00403-z

Cite this

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title = "Solution method for fifth-order fuzzy initial value problem",

abstract = "Fuzzy differential equations (FDEs) are the general concept of ordinary differential equations. FDE seems to be a natural way to model the propagation of cognitive uncertainty in dynamic environments. This article establishes the characteristics of the strongly generalized Hukuhara differentiability (SGHD)-based fifth-order derivative of the fuzzy-valued function (FVF). The Laplace operator is used in SGHD to create a strategy for solving the fifth-order fuzzy initial value problem (FIVP). Furthermore, some examples of FIVP are addressed to exploit liability and the efficiency of our proposed method. Furthermore, the switching points and solutions of FIVP are presented graphically to demonstrate and corroborate the theoretical findings. Additionally, an application of a mass-spring-damper system is solved by our proposed method.",

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author = "Muhammad Akram and Muhammad Yousuf and Muhammad Bilal",

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year = "2023",

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doi = "10.1007/s41066-023-00403-z",

language = "English",

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TY - JOUR

T1 - Solution method for fifth-order fuzzy initial value problem

AU - Akram, Muhammad

AU - Yousuf, Muhammad

AU - Bilal, Muhammad

PY - 2023/11

Y1 - 2023/11

N2 - Fuzzy differential equations (FDEs) are the general concept of ordinary differential equations. FDE seems to be a natural way to model the propagation of cognitive uncertainty in dynamic environments. This article establishes the characteristics of the strongly generalized Hukuhara differentiability (SGHD)-based fifth-order derivative of the fuzzy-valued function (FVF). The Laplace operator is used in SGHD to create a strategy for solving the fifth-order fuzzy initial value problem (FIVP). Furthermore, some examples of FIVP are addressed to exploit liability and the efficiency of our proposed method. Furthermore, the switching points and solutions of FIVP are presented graphically to demonstrate and corroborate the theoretical findings. Additionally, an application of a mass-spring-damper system is solved by our proposed method.

AB - Fuzzy differential equations (FDEs) are the general concept of ordinary differential equations. FDE seems to be a natural way to model the propagation of cognitive uncertainty in dynamic environments. This article establishes the characteristics of the strongly generalized Hukuhara differentiability (SGHD)-based fifth-order derivative of the fuzzy-valued function (FVF). The Laplace operator is used in SGHD to create a strategy for solving the fifth-order fuzzy initial value problem (FIVP). Furthermore, some examples of FIVP are addressed to exploit liability and the efficiency of our proposed method. Furthermore, the switching points and solutions of FIVP are presented graphically to demonstrate and corroborate the theoretical findings. Additionally, an application of a mass-spring-damper system is solved by our proposed method.

KW - Generalized Hukuhara differentiability

KW - Initial-value problem

KW - Mittag–Leffler function

KW - Switching point

UR - https://www.scopus.com/pages/publications/85168658723

U2 - 10.1007/s41066-023-00403-z

DO - 10.1007/s41066-023-00403-z

M3 - Review article

AN - SCOPUS:85168658723

SN - 2364-4966

VL - 8

SP - 1229

EP - 1252

JO - Granular Computing

JF - Granular Computing

IS - 6

ER -

Solution method for fifth-order fuzzy initial value problem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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