Geodesic
Boundary value problem for partial differential equation with fractional Riemann--Liouville derivative
Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 67-72

Voir la notice de l'article provenant de la source Math-Net.Ru

For a differential equation involving a fractional order diffusion equations, we study a non-local problem in an unbounded domain where the boundary condition involves a linear combination of generalized operators of a fractional integro-differentiation. For various values of the parameters of these operators by Tricomi method we prove the uniqueness of solution to the considered problem. The existence of solution is obtained in the closed form as a solution to the appropriate equation with fractional derivative of various order.
Keywords: boundary value problem, generalized operator of fractional integro-differentiation, Wright's function, fractional order differential equation. 
@article{UFA_2015_7_3_a7,
     author = {O. A. Repin},
     title = {Boundary value problem for partial differential equation with fractional {Riemann--Liouville} derivative},
     journal = {Ufa mathematical journal},
     pages = {67--72},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a7/}
}
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O. A. Repin. Boundary value problem for partial differential equation with fractional Riemann--Liouville derivative. Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 67-72. http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a7/