We apply the tools of the fractional calculus to introduce new fractional-order beam solutions to the paraxial wave equation that can be regarded as intermediate solutions between the known integral-order solutions. We restrict our attention to the fractionalization of the elegant and standard Hermite-Gaussian beams.

This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. Special attention is given to numerical computation of fractional derivatives and integ...

In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus.

INTRODUCTION At high b-values (e.g., ≥1,500 s/mm), it is well known that diffusion-induced MR signal loss in the brain tissue exhibits anomalous behavior that cannot be described by a mono-exponential function. This phenomenon has been attributed to tissue heterogeneity manifested by cellular structures, cell membranes, and/or intraand extra-cellular spaces [1]. Over the past few years, a numbe...

This study explores the role that microstructure plays in determining macroscopic static response of porous elastic continua and exposes occurrence position-dependent nonlocal effects are strictly correlated to configuration microstructure. Then, a continuum theory based on variable-order fractional calculus is developed order accurately capture complex spatially distributed response. The remar...

This paper gives sufficient conditions for finite time stability and stabilization for perturbed nonlinear (non)homogeneous fractional order systems with time-varying delay. New stability criteria for this class of fractional order systems were derived using a recently obtained generalized Gronwall inequality as well as “classical” Bellman-Gronwall inequality. Last, a numerical example is given...

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C20, 26A33. Keywords—Fractional Derivatives and Integrals, Hypergeometric functions. THE names fractional calculus is concerned with the ge...

In this paper, we study multi-dimensional wave-like equations with variable coefficients within the frame of fractional calculus using natural decomposition method (FNDM). The considered algorithm is an elegant combination transform and scheme. Five different cases are to illustrate validate competence projected technique in present framework. behaviours obtained results have been captured for ...