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 deriv...

This article is mainly devoted to the study of existence solutions for second-order abstract non-autonomous integro-differential evolution equations with infinite state-dependent delay. In first part, we are concerned retarded functional differential second extend our results neutral Our established using properties resolvent operator corresponding equation and fixed point theorems. Finally, an...

In this article, we consider the analogue of the Dirichlet problem for second-order elliptic integro-differential equations, which consists in imposing the “boundary conditions” in the whole complementary of the domain. We are looking for conditions on the differential and integral parts of the equation in order to ensure that the Dirichlet boundary condition is satisfied in the classical sense...

This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized integro-differential boundary conditions by utilizing contraction principle Banach Leray–Schauder fixed point theorems. Moreover, two different approaches, Hyers–Ulam stabilities are also discussed. Different ordinary third order (e.g., initial, an...

In this paper, univariate Pade approximation is applied to fractional power sries solutions of integro-differential equations with non-local boundary conditions. As it seen from comparisons, gives reliable and numerical results.

A laminar, two dimensional, steady boundary layer Newtonian conducting fluid flow passes over a permeable shrinking sheet in the presence of a uniform magnetic field is investigated. The governing equations have converted to ordinary nonlinear differential equations (ODE) by using appropriate similarity transformations. The main idea is to transform ODE with infinite boundary condition into oth...