Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analyt...

By using the properties of strong fuzzy Henstock integrals, the existence theorems of solution for a kind of the discontinuous fuzzy Fredholm integral equations are established. The results are generalizations of earlier investigation for fuzzy continuous systems.

Nowadays in the complicated systems, design of proper and implementable controller has a most importance. With respect to ability of fractional order systems in complicated systems identification as a first order fractional system with time delay, usage of fractional order PID has a proper result. From one side flexibility of fractional calculus than integer order has been topics of interest to...

We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation values of three Abel integral equations are found, illustrating the effectiveness of the proposed ap...

using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

in this paper we intend to offer new numerical methods to solve the second-order fuzzy abel-volterraintegro-differential equations under the generalized $h$-differentiability. the existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

Abstract The integral transform method based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the generalized Weyl space-fractional operator. The solutions, representing ...