‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

The fractional Laplacian (−�)γ/2 commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < γ < d, its inverse is the classical Riesz potential Iγ which is dilationinvariant and translation-invariant. In this work, we investigate the functional properties (contin...

In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz tra...

We develop criteria for hitting probabilities of anisotropic Gaussian random fields with associated canonical pseudo-metric given by a class gauge functions. This yields lower and upper bounds in terms general notions capacity Hausdorff measure, respectively, therefore extending the classical estimates Bessel-Riesz $\gamma$-dimensional measure. apply to system linear stochastic partial differen...

In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given. 

In this article, we introduce the fractional differential systems in the sense of the Weber fractional derivatives and study the asymptotic stability of these systems. We present the stability regions and then compare the stability regions of fractional differential systems with the Riemann-Liouville and Weber fractional derivatives.