In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional derivative. The peresented solutions for these problems are as infinite series. ‎Convergence‎ of series solutions and uniqueness of them are stablished by general theory of mathematical analysis and theory of ODEs.