fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order.the purpose of this work is to use hadamard fractional integral to establish some new integral inequalities of gruss type by using one or two parameters which ensues four main results . furthermore, other integral inequalities of reverse m...

and Applied Analysis 3 Differential calculus Exponent

We study the existence and monotone iterative approximation of mild solutions fractional-order neutral differential equations involving a generalized fractional derivative order 0 < α 1 which can be reduced to Riemann–Liouville or Hadamard derivatives. The is obtained via fixed point techniq...

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Fell...

In this article, we provide constraints for the sum by employing a generalized modified form of fractional integrals Riemann-type via convex functions. The mean inequalities functions with absolute value derivatives are discovered. Hermite–Hadamard-type symmetric function explored. These results achieved using fresh and innovative methodology integrals. Some applications explored in paper brief...

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

We investigate the macroscopic diffusion of carriers in the multiple-trapping (MT) regime, in relation with electron transport in nanoscaled heterogeneous systems, and we describe the differences, as well as the similarities, between MT and the continuous-time random walk (CTRW). Diffusion of free carriers in MT can be expressed as a generalized continuity equation based on fractional time deri...