In this paper, we consider linear space-time fractional reactiondiffusion equation with composite fractional derivative as time derivative and Riesz-Feller fractional derivative with skewness zero as space derivative. We apply Laplace and Fourier transforms to obtain its solution.

We consider a methodology based in B-splines scaling functions to numerically invert Fourier or Laplace transforms. The methodology is particularly well suited when the original function or its derivatives present peaks or jumps due to discontinuities in the domain.

This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of (FT). The Unilateral Laplace (LT) observed to be special case GFT. GFT, as proposed in this work, contributes significantly scholarly literature. There are many salient contribution work. Firstly, GFT applicable a much larger class signals, some which cannot analyzed with FT and LT. For examp...

We discuss and derive the analytical solution for three basic problems of the so-called timefractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in...

Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotiv...

The theory of fuzzy transform (F-transform, for short) has been developed extensively in recent years. Based on the current successes of F-transform, we expect that in the future, F-transform will become as successful and as widely used as the well-known transforms such as Laplace, Fourier, and wavelet transforms. The most successful applications of F-transform are in the fields of image proces...

In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal processing. The well-known integral transforms: Fourier, fractional Fourier, bilateral Laplace and Fresnel transforms are special cases of the LCT. In this p...