TY - JOUR
T1 - TWO-DIMENSIONAL FRACTIONAL WAVE EQUATION VIA A NEW NUMERICAL APPROACH
AU - Batiha, Iqbal M.
AU - Jebril, Iqbal H.
AU - Anakira, Nidal
AU - Al-Nana, Abeer A.
AU - Batyha, Radwan
AU - Momani, Shaher
N1 - Publisher Copyright:
© ICIC International 2024.
PY - 2024/8
Y1 - 2024/8
N2 - The main goal of this work is to solve the fractional wave equation in two dimensions numerically with the use of some novel fractional formulas. In particular, the proposed approach used to deal with the fractional wave equation introduces two novel fractional difference formulas for approximating the Caputo differentiator of order δ and 2δ, respectively, where 0 < δ ≤ 1. Such formulas, which are derived based on the Lagrange interpolating polynomial, can generate a system of linear equations that can be solved numerically to obtain, ultimately, good approximate solutions to the fractional wave equation for different fractional-order values.
AB - The main goal of this work is to solve the fractional wave equation in two dimensions numerically with the use of some novel fractional formulas. In particular, the proposed approach used to deal with the fractional wave equation introduces two novel fractional difference formulas for approximating the Caputo differentiator of order δ and 2δ, respectively, where 0 < δ ≤ 1. Such formulas, which are derived based on the Lagrange interpolating polynomial, can generate a system of linear equations that can be solved numerically to obtain, ultimately, good approximate solutions to the fractional wave equation for different fractional-order values.
KW - Fractional calculus
KW - Fractional difference formula
KW - Lagrange interpolating polynomial
KW - Two-dimensional fractional wave equation
UR - http://www.scopus.com/inward/record.url?scp=85200570649&partnerID=8YFLogxK
U2 - 10.24507/ijicic.20.04.1045
DO - 10.24507/ijicic.20.04.1045
M3 - Article
AN - SCOPUS:85200570649
SN - 1349-4198
VL - 20
SP - 1045
EP - 1059
JO - International Journal of Innovative Computing, Information and Control
JF - International Journal of Innovative Computing, Information and Control
IS - 4
ER -