Description The book presents a collection of papers prepared on the basis of plenary invited lectures at the ninth International Workshop “Analytic Methods of Analysis and Differential Equations”, dedicated to 70th anniversary of Professor Anatoly Kilbas (1948-2010) The Workshop was held in Minsk, Belarus in September 2018 and covered key topics and Analysis and Differential Equations, including fractional calculus and fractional differential equations, integral transforms, factorization of matrix-functions and vector-matrix boundary value problems, elliptic and parabolic partial differential equations, linear and nonlinear ordinary differential equations and systems treated by exact and numerical methods. Special attention is given to the applications of the developed technique to the study of problems of mechanics, biomechanics, medicine and economics.