Fractional calculus with power law: The cradle of our ancestors⋆

Abstract

The application of differential operators based on convolution settings has become the centre of investigation of researchers from all the corners of the globe. Several discussions have been raised and many suggestions have been done. The aim of this paper is to answer some outstanding questions that have been asked and also correct some claims that have been made for many years within the field. We have, in addition to this, suggested some fractional operators that could be used in the future for modelling and theoretical investigations. We have constructed a new class of partial integro-differential equations with fractional operators based on the new generalized Mittag-Leffler function. We presented a detailed discussion underpinning the conditions for which the new equation is well-posed. We suggested to solve this equation, a new numerical methodology that will be used to handle such equation numerically.