Abstract The research of a formulation to model non-local interactions in the mechanical behavior matter is currently an open problem. In this context, strong based on fractional calculus provided paper. This derived from analogy with long-memory viscoelastic models. Specifically, same kind power-law time-dependent kernel used Boltzmann integral stress-strain relation as Fredholm relation. lead...

The method ot atomic decomposition of Besov and Lizorkin-Triebel function spaces is combined with basic ideas from the theory of singular integral operators and applied to the study of fractional integral and diierential operators (FIDO), of which the Riesz potential is considered in detail as a model example. The main new results are: characterization of the Riesz potential by an innnite-dimen...

‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative ‎examples.‎

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

Differential problems with the Riesz derivative in space are widely used to model anomalous diffusion. Although Riesz–Caputo is more suitable for modeling real phenomena, there few examples literature where numerical methods solve such differential problems. In this paper, we propose approximate of a given function cubic spline. As far as aware, first time that splines have been context derivat...

in this paper, the dynamical behavior of an axially moving string modeled by fractional derivative is investigated. the governing equation represented motion is solved by the method of multiple scales. considering principal parametric resonance, the stability boundaries for string with simple supports are obtained. numerical results indicate the effects of fractional damping on stability.

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

We introduce and study a topological structure over vectorial and Riesz MV-algebras, similar to metric spaces. Continuous functions with values in these spaces are studied and a fix point theorem is obtained. Moreover we introduce the concept of derivative and integral of MV-valued functions; i.e. functions with values in a Riesz MV-algebra. Finally we present two applications. 2003 Elsevier In...

in this work, we have applied elzaki transform and he's homotopy perturbation method to solvepartial dierential equation (pdes) with time-fractional derivative. with help he's homotopy per-turbation, we can handle the nonlinear terms. further, we have applied this suggested he's homotopyperturbation method in order to reformulate initial value problem. some illustrative examples...