The Solution to Impulse Boundary Value Problem for a Class of Nonlinear Fractional Functional Differential Equations

In this paper, we investigate the existence of solution for a class of impulse boundary value problem of nonlinear fractional functional differential equation of mixed type. We obtain the existence results of solution by applying some well-known fixed point theorems. An example is given to illustrate the effectiveness of our result.

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel’skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results.

EXISTENCE RESULTS FOR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH RIEMANN-LIOUVILLE DERIVATIVE

In this paper, using the contracting mapping principle and the monotone iterative method, we consider the existence of solution to the initial value problem of fractional functional differential equations with Riemann-Liouville derivative.

Computable extensions of generalized fractional kinetic equations in astrophysics

Fractional calculus and special functions have contributed a lot to mathematical physics and its various branches. The great use of mathematical physics in distinguished astrophysical problems has attracted astronomers and physicists to pay more attention to available mathematical tools that can be widely used in solving several problems of astrophysics/physics. In view of the great importance and usefulness of kinetic equations in certain astrophysical problems, the authors derive a generalized fractional kinetic equation involving the Lorenzo-Hartley function, a generalized function for fractional calculus. The fractional kinetic equation discussed here can be used to investigate a wide class of known （and possibly also new） fractional kinetic equations, hitherto scattered in the literature. A compact and easily computable solution is established in terms of the Lorenzo-Hartley function. Special cases, involving the generalized Mittag-Leffler function and the R-function, are considered. The obtained results imply the known results more precisely.

EXISTENCE OF MILD SOLUTIONS TO SEMILINEAR FRACTIONAL ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a Banach space.

Existence of p-mean Almost Periodic Mild Solution for Fractional Stochastic Neutral Functional Differential Equation

A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis theory,a sufficient condition of the existence for p-mean almost periodic solution is obtained,which are supported by two examples.

CAUCHY PROBLEM FOR FRACTIONAL BEAM-LIKE EQUATIONS

In one space-and in one time -dimension a beam-like equation is solved, where the second time derivative is replaced by the α- fractional time derivative, 1 〈 α ≤ 2. The solution is given in closed form in terms of the Mttag-Leffler functions in two parameters.