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Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics
Abstract.We revisit the Mittag-Leffler functions of a real variable t, with one, two and three order-parameters {α,β,γ}, as far as their Laplace transform pairs and complete monotonicity propertiesExpand
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Resistive Plates Carrying a Steady Current: Electric Potential and Surface Charges Close to the Battery
We treat the problem of two resistive plates carrying a steady current in the same direction. We consider a linear battery orthogonal to the direction of the current in the middle of the plates. WeExpand
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A real integral by means of complex integration
This note presents and discusses a class of real integrals involving a hyperbolic function by means of complex integration. An integral representation is obtained which appears in several fields ofExpand
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On exact and inexact differentials and applications
ABSTRACT Considering the important role played by mathematical derivatives in the study of physical–chemical processes, this paper discusses the different possibilities and formulations of thisExpand
On an integral with two branch points
The paper considers a class of real integrals performed by using a convenient integral in the complex plane. A complex integral containing a multi-valued function with two branch points isExpand
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Some properties of the El n (r) polynomials
We present a new class of polynomials that are solutions of the generalized Laplace differential equation, written in spherical coordinates. Differentiation properties, orthogonality, Rodrigues likeExpand
Is a definition always useful to calculate something?
We calculate the limit of a particular trigonometric function After a question proposed by a student: can you show a particular result, involving a trigonometric limit, using the definition of limit?Expand
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One-sided and two-sided Green’s functions
We discuss the one-sided Green’s function, associated with an initial value problem and the two-sided Green’s function related to a boundary value problem. We present a specific calculationExpand
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Faedo-Galerkin approximation of mild solutions of fractional functional differential equations
Abstract In the paper, we discuss the existence and uniqueness of mild solutions of a class of fractional functional differential equations in Hilbert space separable using the Banach fixed pointExpand