In this paper, in the class of smooth functions, integration and differentiation operators connected with fractional conformable derivatives are introduced. The mutual reversibility these is proved, properties functions studied. Using transformations generalizing involutive transformations, a nonlocal analogue Laplace operator For corresponding Poisson equation, solvability some boundary value ...

  Abstract.   The Sturm-Liouville boundary value problem of the multi-order fractional differential equation  is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems.

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional diff<span style="font-family: NimbusRomNo...