TY - JOUR
ID - 17827
TI - A unified Explicit form for difference formulas for fractional and classical derivatives and applications
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Gunarathna, W. Anura
AU - Nasir, Haniffa Mohamed
AU - Daundasekera, Wasantha B.
AD - Department of Physical Sciences, College of Applied Sciences,
Rajarata University, Sri Lanka.
AD - FracDiff Research Group, Department of Mathematics, P. O. Box: 36, Sultan Qaboos University, Al-Khoud 123, Muscat, Sultanate of Oman.
AD - Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka.
Y1 - 2024
PY - 2024
VL -
IS -
SP -
EP -
KW - Fractional derivative
KW - Shifted Gr"unwald approximation
KW - Lubich Generators
KW - Compact finite difference formula
KW - Boundary value problem
DO - 10.22034/cmde.2023.58229.2459
N2 - A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivative with a desired order of accuracy at any nodal point in the computational domain. It also gives Gr\"unwald type approximations for fractional derivatives with arbitrary order of approximation at any point. Thus, this explicit unifies approximations of both types of derivatives. Moreover, for classical derivatives, it provides various finite difference formulas such as forward, backward, central, staggered, compact, non-compact, etc. Efficient computations of the coefficients of the difference formulas are also presented that lead to automating the solution process of differential equations with a given higher order accuracy. Some basic applications are presented to demonstrate the usefulness of this unified formulation.
UR - https://cmde.tabrizu.ac.ir/article_17827.html
L1 - https://cmde.tabrizu.ac.ir/article_17827_625e23ec220556744eb5a69d35ad943b.pdf
ER -