The Insistence of God: A Theology of Perhaps

Title: The insistence of God: a theology of perhaps. Author: John D Caputo. Publisher: Bloomington : Indiana University Press, 2013. ISBN: 978025301010

On the new properties of Caputo–Fabrizio operator and its application in deriving shifted Legendre operational matrix

In this paper, we study the recently introduced Caputo and Fabrizio operator, which this new operator was derived by replacing the singular kernel in the classical Caputo derivative with the regular kernel. We introduce some useful properties based on the definition by Caputo and Fabrizio for a general order n < α < n + 1, n ∈ N. Here, we extend the associated integral of Caputo–Fabrizio sense to n < α < n + 1, n ∈ N. We also find the general formula for the Caputo–Fabrizio operator of (t − a)β . Then, we derive Legendre operational matrix based on this new operator and together with Tau method, we use it to solve the differential equations defined in the Caputo–Fabrizio sense. As far as we know, the operational matrix method has yet been derived or attempted for solving the differential equations in Caputo–Fabrizio sense, while it has been successfully used to solve fractional calculus problems involving the classical Caputo sense. Some numerical examples are given to display the simplicity and accuracy of the proposed technique

On fractional derivatives and primitives of periodic functions

In this paper we prove that the fractional derivative or the fractional primitive of a $T$-periodic function cannot be a $\tilde{T}$-periodic function, for any period $\tilde{T}$, with the exception of the zero function.Comment: 12 page