Related papers: Fractional differential relations for the Lerch ze…
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the…
In this paper, certain generalized fractional derivative formulae are introduced involving the k-Mittag-Leffler function. Then their image formulae (using Beta transform, Laplace transform and Whittaker transform) are also established. The…
We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these…
We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
This note contains a short proof of the functional equation for the zeta function.
There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the…
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…
This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…
The connection between Lefschetz formulae and zeta function is explained. As a particular example the theory of the generalized Selberg zeta function is presented. Applications are given to the theory of Anosov flows and prime geodesic…
The GUE Hypothesis, which concerns the distribution of zeros of the Riemann zeta-function, is used to evaluate some integrals involving the logarithmic derivative of the zeta-function. Some connections are shown between the GUE Hypothesis…
We derive new reduction formulas for the incomplete beta function and the Lerch transcendent in terms of elementary functions. As an application, we calculate some new integrals. Also, we use these reduction formulas to test the performance…
We explore Fourier transforms of the reciprocal of the Riemann zeta function that have connections to the RH. A partial answer to a recently posed problem is explored by exploiting the fact that $\zeta(s)\neq0$ when $\Re(s)=1.$
We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.
In this work we argue about the Lesche stability of some systems, that are motivated by the use of fractional derivatives.
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
In a recent paper, Cohl and Costas-Santos derived a number of interesting multi-derivative and multi-integral relations for associated Legendre and Ferrers functions in which the orders of those functions are changed in integral steps.…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…