Gellerstedt Type Problem for the Loaded Parabolic-Hyperbolic Type Equation with Caputo and Erdelyi–Kober Operators of Fractional Order

Extension of the Tricomi problem for a loaded parabolic–hyperbolic equation with a characteristic line of change of type

“…Problem $$$ {T}_1 $$$ in case $$$ n=1 $$$ was first posed and investigated by Gellerstedt for the classical mixed‐type equation. For a loaded equation, the Gellerstedt problem was studied in Baltaeva and Pedro and Abdullaev and Islomov 26,27 . The present generalized type of problem $$$ {T}_1 $$$ for the classical equation of elliptic–hyperbolic type was proposed in the works of Djuraev and Sopuev, Mirsaburov et al, and Bitsadze 25,28,29 …”

“…We should note recent publications [5][6][7][8][15][16][17][18][19][20][21][22][23][24] solved the most important boundary value problems for the differential equations parabolic, hyperbolic, and parabolic-hyperbolic types with fractional derivative in the sense of Riemann-Liouville and Caputo.…”

“…For a loaded equation, the Gellerstedt problem was studied in Baltaeva and Pedro and Abdullaev and Islomov. 26,27 The present generalized type of problem T 1 for the classical equation of elliptic-hyperbolic type was proposed in the works of Djuraev and Sopuev, Mirsaburov et al, and Bitsadze. 25,28,29 Remark 1.…”