Department of Mathematics and Sciences Dhofar University, Salalah Oman [email protected] Abstract Legendre wavelets methods are commonly used for the numerical solution of integral equations. In this paper, we apply the Legendre wavelets method to approximate the solution of fractional integro-differential equations. Numerical examples are also presented to demonstrate the validity of the method....

In this investigation, we have established the existence and uniqueness results of solutions for class of an abstract fractional functional integro-differential equations with state dependent delay subject to not instantaneous impulse by using fixed point theorems. One example is presented to illustrate the main results of the paper. MSC: 26A33 • 34K05 • 34A12 • 26A33

An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for temporal semidiscretization of the problem. Stability estimates of the discrete problem are proved, that are used to prove optimal order a priori error estimate...

In this paper, we consider an anti-periodic Boundary Value Problem for Volterra integro-differential equation of fractional order 1 < α ≤ 2, with generalized Mittag-Leffler function in the kernel. Some existence and uniqueness results are obtained by using some well known fixed point theorems. We give some examples to exhibit our results. c ©2016 All rights reserved.

This paper is concerned with the controllability result of mild solution for an impulsive neutral fractional order stochastic integro-differential equation with infinite delay subject to nonlocal conditions. The existence result is obtained by using the fixed point technique on a Hilbert space. At last, we present an example to verify the result. MSC: 93B05 • 26A33 • 34K05 • 34A37 • 34K50

In this article, we deal with the existence of mild solutions for a class of fractional integro-differential equations with state-dependent delay. Our results are based on the technique of measures of noncompactness and Darbo’s fixed point theorem. An example is provided to illustrate the main result. AMS Subject Classifications: 26A33, 34A08, 34A37, 34G20, 34G25, 34H05, 34K09, 34K30.

In this expository paper we discuss the boundary regularity of solutions to Lu = f(x, u) in Ω, u ≡ 0 in R\Ω, present the Pohozaev identities recently established in [17, 21], and give a sketch of their proofs. The operators L under consideration are integro-differential operator of order 2s, s ∈ (0, 1), the model case being the fractional Laplacian L = (−∆).

Fractional calculus differentiation and integration of arbitrary order is proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos. In fact, this branch of calculus has found its applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and i...