Boundary Value Problems and Applications for Mixed Type Loaded PDEs

This book is devoted to the analytical study of boundary value problems for third-order parabolic-hyperbolic equations containing nonlocal and fractional loaded terms.It develops a unified analytical framework for the investigation of local and nonlocal formulations, bringing together classical partial differential equation theory and fractional calculus.Particular attention is paid to the solvability theory of Tricomi-, Gellerstedt-, and Darboux-type problems, including the establishment of existence and uniqueness theorems and the derivation of explicit solution representations. The book extends traditional models through the incorporation of Riemann-Liouville fractional integro-differential operators and explores the connections between local and nonlocal formulations by means of integral transformation techniques and inverse problem methods.Special emphasis is placed on reduction procedures that transform third-order equations into lower-order systems, facilitating rigorous analyti