, BOUNDARY VALUE PROBLEM FOR THE LOADED EQUATION OF FRACTIONAL ORDER WITH FORWARD AND BACKWARD TIME STEPPING // BSU Bulletin. Mathematics, Informatics. - 2017. №4. . - С. 3-8.

BOUNDARY VALUE PROBLEM FOR THE LOADED EQUATION OF FRACTIONAL ORDER WITH FORWARD AND BACKWARD TIME STEPPING

DOI: 10.18101/2304-5728-2017-4-3-8 UDK: 517.95

The article considers a boundary value problem for the loaded parabolic equation involving the Riemann – Liouville derivative with forward and back- ward time stepping in a rectangular domain. It is proved that the problem is uniquely solvable for the class of functions satisfying the Holder condition. The issue on the solvability of the problem can be reduced to the solvability of the generalized Abel equation, and therefore to the solvability of the singular inte- gral equation.

mixed parabolic equation; the Gevrey problem; loaded equation; the Riemann-Liouville fractional integral operator; fractional diffusion equation; the Volterra integral equation; the Wright-type function, the Abel equation, the Holder condition.