In this paper, we apply fractional complex transform to convert the fractional nonlinear Schr"{o}dinger equations to the nonlinear Schr"{o}dinger equations.  

In this paper multistep methods for systems of coupled second order Volterra integrodifferential equations are proposed. Stability and convergence properties are studied and an error bound for the discretization error is given.

This paper is concerned with delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. Using the theory of semigroups and the method of fixed points, existence results are obtained for mild solutions.

This paper investigates the fixed points for self-maps of a closed set in a space of abstract continuous functions. Our main results essentially extend the Banach contracting mapping principle. An application to integrodifferential equations is given.

We establish conditions for the existence of solutions weakly perturbed impulsive boundary-value problems systems integrodifferential equations and determine structure these solutions. The sufficient condition are investigated with help theory orthoprojectors pseudoinverse Moore–Penrose matrices.

in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

in this paper, the sinc collocation method is proposed for solving linear and nonlinear multi-order fractional differential equations based on the new definition of fractional derivative which is recently presented by khalil, r., al horani, m., yousef, a. and sababeh, m. in a new definition of fractional derivative, j. comput. appl. math. 264 (2014), 65{70. the properties of sinc functions are ...