Numerical solution of second-order fuzzy differential equation of integer and fractional order using reproducing kernel hilbert space method tools

Asia Khalaf Albzeirat; Muhammad Zaini Ahmad; Shaher Momani; Banan Maayah

doi:10.17654/MS101061327

Numerical solution of second-order fuzzy differential equation of integer and fractional order using reproducing kernel hilbert space method tools

Asia Khalaf Albzeirat
, Muhammad Zaini Ahmad
, Shaher Momani
, Banan Maayah

Universiti Malaysia Perlis
University of Jordan
Faculty of Sciences, King Abdulaziz University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper presents a numerical solution procedure for solving secondorder differential equation of integer and fractional order subject to fuzzy conditions. The procedure is based on the usage of tools of reproducing kernel Hilbert space in which every function satisfies the initial fuzzy conditions in the second-order differential equation. The procedure produces solutions of high accuracy and examples are provided to illustrate the effectiveness of the solution procedure. The proposed procedure is flexible and has the potential to be further employed to solve problems involving other levels of order in fractional calculus subject to fuzzy conditions.

Original language	English
Pages (from-to)	1327-1351
Number of pages	25
Journal	Far East Journal of Mathematical Sciences
Volume	101
Issue number	6
DOIs	https://doi.org/10.17654/MS101061327
State	Published - Mar 2017
Externally published	Yes

Keywords

Caputo fractional derivative
Fractional calculus
Fuzzy differential equation of integer and fractional order
Reproducing kernel Hilbert space method

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10.17654/MS101061327

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title = "Numerical solution of second-order fuzzy differential equation of integer and fractional order using reproducing kernel hilbert space method tools",

abstract = "This paper presents a numerical solution procedure for solving secondorder differential equation of integer and fractional order subject to fuzzy conditions. The procedure is based on the usage of tools of reproducing kernel Hilbert space in which every function satisfies the initial fuzzy conditions in the second-order differential equation. The procedure produces solutions of high accuracy and examples are provided to illustrate the effectiveness of the solution procedure. The proposed procedure is flexible and has the potential to be further employed to solve problems involving other levels of order in fractional calculus subject to fuzzy conditions.",

keywords = "Caputo fractional derivative, Fractional calculus, Fuzzy differential equation of integer and fractional order, Reproducing kernel Hilbert space method",

author = "Albzeirat, \{Asia Khalaf\} and Ahmad, \{Muhammad Zaini\} and Shaher Momani and Banan Maayah",

note = "Publisher Copyright: {\textcopyright} 2017 Pushpa Publishing House, Allahabad, India.",

year = "2017",

month = mar,

doi = "10.17654/MS101061327",

language = "English",

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pages = "1327--1351",

journal = "Far East Journal of Mathematical Sciences",

issn = "0972-0871",

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Numerical solution of second-order fuzzy differential equation of integer and fractional order using reproducing kernel hilbert space method tools. / Albzeirat, Asia Khalaf; Ahmad, Muhammad Zaini; Momani, Shaher et al.
In: Far East Journal of Mathematical Sciences, Vol. 101, No. 6, 03.2017, p. 1327-1351.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Numerical solution of second-order fuzzy differential equation of integer and fractional order using reproducing kernel hilbert space method tools

AU - Albzeirat, Asia Khalaf

AU - Ahmad, Muhammad Zaini

AU - Momani, Shaher

AU - Maayah, Banan

PY - 2017/3

Y1 - 2017/3

N2 - This paper presents a numerical solution procedure for solving secondorder differential equation of integer and fractional order subject to fuzzy conditions. The procedure is based on the usage of tools of reproducing kernel Hilbert space in which every function satisfies the initial fuzzy conditions in the second-order differential equation. The procedure produces solutions of high accuracy and examples are provided to illustrate the effectiveness of the solution procedure. The proposed procedure is flexible and has the potential to be further employed to solve problems involving other levels of order in fractional calculus subject to fuzzy conditions.

AB - This paper presents a numerical solution procedure for solving secondorder differential equation of integer and fractional order subject to fuzzy conditions. The procedure is based on the usage of tools of reproducing kernel Hilbert space in which every function satisfies the initial fuzzy conditions in the second-order differential equation. The procedure produces solutions of high accuracy and examples are provided to illustrate the effectiveness of the solution procedure. The proposed procedure is flexible and has the potential to be further employed to solve problems involving other levels of order in fractional calculus subject to fuzzy conditions.

KW - Caputo fractional derivative

KW - Fractional calculus

KW - Fuzzy differential equation of integer and fractional order

KW - Reproducing kernel Hilbert space method

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U2 - 10.17654/MS101061327

DO - 10.17654/MS101061327

M3 - Article

AN - SCOPUS:85015946158

SN - 0972-0871

VL - 101

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EP - 1351

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

IS - 6

ER -

Numerical solution of second-order fuzzy differential equation of integer and fractional order using reproducing kernel hilbert space method tools

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Keywords

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