Geodesic
On a problem for mixed type equation with partial Riemann--Liouville fractional derivative
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 4, pp. 636-643

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The uniqueness and existence of solutions of a nonlocal problem proved for an equation of mixed type. This equation contains diffusion equation of fractional order. The boundary condition contains a linear combination of generalized operators of fractional order with the Gauss hypergeometric function. The solution of the problem is given explicitly.
Keywords: boundary value problem, generalized fractional integro-differentiation operator, differential equation of fractional order, Gauss hypergeometric function. 
@article{VSGTU_2016_20_4_a4,
     author = {O. A. Repin and A. V. Tarasenko},
     title = {On a problem for mixed type equation with partial {Riemann--Liouville} fractional derivative},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {636--643},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2016_20_4_a4/}
}
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O. A. Repin; A. V. Tarasenko. On a problem for mixed type equation with partial Riemann--Liouville fractional derivative. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 4, pp. 636-643. http://geodesic.mathdoc.fr/item/VSGTU_2016_20_4_a4/