TY - JOUR
T1 - An analytical study of physical models with inherited temporal and spatial memory
AU - Jaradat, Imad
AU - Alquran, Marwan
AU - Al-Khaled, Kamel
N1 - Publisher Copyright:
© 2018, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/4/1
Y1 - 2018/4/1
N2 - Du et al. (Sci. Reb. 3, 3431 (2013)) demonstrated that the fractional derivative order can be physically interpreted as a memory index by fitting the test data of memory phenomena. The aim of this work is to study analytically the joint effect of the memory index on time and space coordinates simultaneously. For this purpose, we introduce a novel bivariate fractional power series expansion that is accompanied by twofold fractional derivatives ordering α, β∈ (0 , 1 ]. Further, some convergence criteria concerning our expansion are presented and an analog of the well-known bivariate Taylor’s formula in the sense of mixed fractional derivatives is obtained. Finally, in order to show the functionality and efficiency of this expansion, we employ the corresponding Taylor’s series method to obtain closed-form solutions of various physical models with inherited time and space memory.
AB - Du et al. (Sci. Reb. 3, 3431 (2013)) demonstrated that the fractional derivative order can be physically interpreted as a memory index by fitting the test data of memory phenomena. The aim of this work is to study analytically the joint effect of the memory index on time and space coordinates simultaneously. For this purpose, we introduce a novel bivariate fractional power series expansion that is accompanied by twofold fractional derivatives ordering α, β∈ (0 , 1 ]. Further, some convergence criteria concerning our expansion are presented and an analog of the well-known bivariate Taylor’s formula in the sense of mixed fractional derivatives is obtained. Finally, in order to show the functionality and efficiency of this expansion, we employ the corresponding Taylor’s series method to obtain closed-form solutions of various physical models with inherited time and space memory.
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U2 - 10.1140/epjp/i2018-12007-1
DO - 10.1140/epjp/i2018-12007-1
M3 - Article
AN - SCOPUS:85045968262
SN - 2190-5444
VL - 133
JO - European Physical Journal Plus
JF - European Physical Journal Plus
IS - 4
M1 - 162
ER -