On a non-local boundary problem for a parabolic–hyperbolic equation involving a Riemann–Liouville fractional differential operator

Boundary‐value problems for the third‐order loaded equation with noncharacteristic type‐change boundaries

“…The existence and uniqueness of solutions to initial and boundary-value problems for fractional differential equations have been extensively studied by many authors. It should be noted that boundary-value problems for the mixed-type equations involving the Caputo and the Riemann-Liouville fractional differential operators were investigated in previous studies [27][28][29][30] in which uniqueness solvability was proved by the method of integral equations. This method is widely used by many researchers to study boundary-value problems for the mixed-type equations involving the Caputo and the Riemann-Liouville fractional differential operators.…”

Solvability of a Non-local Problem with Integral Transmitting Condition for Mixed Type Equation with Caputo Fractional Derivative

“…Precisely, in [8] the Tricomi and Gellerstedt problem for parabolic-hyperbolic equation with the Riemann-Liouvill fractional operator in the hyperbolic part were under discussion and unique solvability of these problems were proved. In [9] authors consider the same equation, but with two lines of type-changing in a domain with deviation from the characteristics. In above-mentioned works, authors used special transmitting conditions on type-changing lines.…”

Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations

“…Omitting many papers on direct boundary problems for PDEs involving fractional differential operators, we note some works [1][2][3], where time-fractional parabolichyperbolic type equations were investigated. Precisely, main boundary problems for mixed parabolic-hyperbolic equations with the Riemann-Liouville fractional differential operator in parabolic part, were objects of investigations.…”

“…There exist many types of gluing conditions such as continuous, discontinuous, integral form and etc. For instance, in the works [2,3] gluing conditions of integral form were in use, but in the work [5] authors consider boundary problems with continuous gluing conditions, i.e values of seeking function and its derivative from the both parabolic and hyperbolic parts of mixed domain are equal on the line of type changing. Depending on which gluing conditions are used, solvability conditions to given data vary.…”