The properties of Bessel-type fractional derivatives and integrals

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b

Finite-Generalized-Laplace-Hankel-Clifford-Transformation

In this paper, finite-generalized-Laplace-Hankel-Clifford-transformation is established. The relation of the conventional Laplace transformation is applied over finite-generalized-Hankel-Clifford and derived further results. Analyticity and boundedness condition is established. The Operation transform and an inversion formula for a distributional finite-generalized-Laplace-Hankel-Clifford-transformation is developed. A problem is solved in the text to support development of the finite-generalized-Laplace-Hankel-Clifford-transformation

Continuous Generalized Hankel-type integral wavelet transformation

Using the theory of Hankel-type convolution, continuous generalized Hankel-type  wavelet integral transformation is defined. The generalized Hankel-type integral wavelet transformation is developed.  Using the developed theory of generalized Hankel-type convolution, the generalized Hankel-type translation is introduced. Properties of the kernel  are developed in the study. Using the properties of kernel,D Î¼,α, Î² ,v (x,y,z)the generalized Hankel-type wavelet transformation is defined. The existence of the generalized Hankel-type integral wavelet transformation is given by a theorem. The boundedness and inversion formula for the generalized Hankel-type integral wavelet transformation is obtained. A basic wavelet which defines continuous generalized Hankel-type integral wavelet transformation, its admissibility conditions and the wavelet to the function is proved. Examples have been shown to explain the studied continuous generalized Hankel-type integral wavelet transformation. &nbsp