Abstract
We investigate a boundary value problem for partial differential equation with Cauchy-Euler fractional operator x2αD∗,x2αu(x,y)+xαD∗,xαu(x,y)+uyy(x,y)=f(x,y),0<x<∞,0<y<1,0<α<1.The limitations on convergence of series and the Mellin transform lead to the search for solutions in the class of functions, which possess continuous fractional derivatives for x∈ (0 , 1) and equal to zero for x> 1. However, for some cases, the solution is found for the entire semi-infinite strip x> 0. The analysis is supported by the computations, which exhibit the high level of accuracy.
Original language | English |
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Pages (from-to) | 285-294 |
Number of pages | 10 |
Journal | Journal of Mathematical Sciences (United States) |
Volume | 266 |
Issue number | 2 |
DOIs | |
State | Published - Sep 2022 |
Keywords
- Fractional Cauchy-Euler equation
- Fractional partial differential equation
- Mellin transform