An analytical study of physical models with inherited temporal and spatial memory

摘要: Du et al. (Sci. Reb. 3, 3431 (2013)) demonstrated that the fractional derivative order can be physically interpreted as a memory index by fitting test data of phenomena. The aim this work is to study analytically joint effect on time and space coordinates simultaneously. For purpose, we introduce novel bivariate power series expansion accompanied twofold derivatives ordering $\alpha$ , $\beta\in(0,1]$ . Further, some convergence criteria concerning our are presented an analog well-known Taylor’s formula in sense mixed obtained. Finally, show functionality efficiency expansion, employ corresponding method obtain closed-form solutions various physical models with inherited memory.