Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative.

In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grünwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation.

A novel computational approach to approximate fuzzy interpolation polynomials.

This paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form [Formula: see text] where [Formula: see text] is crisp number (for [Formula: see text], which interpolates the fuzzy data [Formula: see text]. Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients of fuzzy polynomial are estimated by the neural network. The numeral experimentations portray that the present interpolation methodology is reliable and efficient.

Fractional calculus and application of generalized Struve function.

A new generalization of Struve function called generalized Galué type Struve function (GTSF) is defined and the integral operators involving Appell's functions, or Horn's function in the kernel is applied on it. The obtained results are expressed in terms of the Fox-Wright function. As an application of newly defined generalized GTSF, we aim at presenting solutions of certain general families of fractional kinetic equations associated with the Galué type generalization of Struve function.

On two fractional differential inclusions.

We investigate in this manuscript the existence of solution for two fractional differential inclusions. At first we discuss the existence of solution of a class of fractional hybrid differential inclusions. To illustrate our results we present an illustrative example.