This paper studies a fractional Bloch equation pertaining to Hilfer operator. is broadly applied in physics, chemistry, nuclear magnetic resonance (NMR), imaging (MRI) and many more. The sumudu transform technique obtain the analytic solutions for magnetization M = ( x , y z ). general solution of shown terms Mittag-Leffler (ML) type function. influence order operator on demonstrated graphical ...

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

is obtained by applying successive integration by parts to the integral represented by the left-hand member of this equation so that the new integrand is the product of F by [(1 —x2)P„' ]', and by replacing this second factor by — n(n + l)Pn according to Legendre's differential equation [l]. Thus certain boundary value problems in ordinary and partial differential equations that involve the dif...