Monotone Solution of Cauchy Type Weighted Nonlocal Fractional Differential Equation

Neumann-Series Solution of Fractional Differential Equation

Bounds on the solution of a Cauchy-type problem involving a weighted sequential fractional derivative

In this paper we establish some bounds for the solution of a Cauchy-type problem for a class of fractional differential equations with a weighted sequential fractional derivative. The bounds are based on a Bihari-type inequality and a bound on Gauss hypergeometric function.

Existence and approximation of solution to neutral fractional differential equation with nonlocal conditions

Keywords: Analytic semigroup Banach fixed point theorem Caputo derivative Faedo–Galerkin approximations Nonlocal conditions Neutral fractional differential equation a b s t r a c t This paper is concerned with the approximation of the solution for neutral fractional differential equation with nonlocal conditions in an arbitrary separable Hilbert space H. We study an associated integral equation...

A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

Mild Solution for Nonlocal Fractional Functional Differential Equation with not Instantaneous Impulse

In the last few decades fractional differential equations are more interested in developing the numerical methods and theoretical analysis, because it is recently proved that it has memory and hereditary property which is valuable in serval field of engineering and sciences. For some recent development theory and applications of fractional differential equations reader can see the monographs [1...