6 documents found, page 1 of 1
Factorization à la Dirac applied to the time-fractional telegraph equation
Ferreira, M.; Rodrigues, M.M.; Vieira, N.This paper examines a coupled system of two-term time-fractional diffusion Dirac-type equations. The system is derived by factorizing the multi-dimensional time-fractional telegraph equation with Hilfer fractional derivatives, using the Dirac method and a triplet of Pauli matrices. Solutions are obtained using operational methods provided by the combination of the Fourier transform in the space variable and the...
Some representations for the eigenfunctions of the time-fractional wave operator
Rodrigues, M.M.; Ferreira, M.; Vieira, NelsonIn this work we present some new representations for the eigenfunctions of the time-fractional wave operator with the time-fractional derivative in the Caputo sense.
Psi-Hilfer fractional relaxation-oscillation equation
Vieira, N.; Ferreira, M.; Rodrigues, M.M.In this work, we solve the ψ-Hilfer fractional relaxation-oscillation equation with a force term, where the time-fractional derivatives are in the ψ-Hilfer sense. The solution of the equation is presented in terms of bivariate Mittag-Leffler functions. An asymptotic analysis of the solution of the associated homogeneous equation is performed.
Aveiro discretization method in mathematics: a new discretization principle
Castro, L.P.; Fujiwara, H.; Rodrigues, M.M.; Saitoh, S.; Tuan, V.K.We found a very general discretization method for solving wide classes of mathematical problems by applying the theory of reproducing kernels. An illustration of the generality of the method is here performed by considering several distinct classes of problems to which the method is applied. In fact, one of the advantages of the present method -- in comparison to other well-known and well established methods --...
Initial value problems in linear integral operator equations
Castro, L.P.; Rodrigues, M.M.; Saitoh, S.For some general linear integral operator equations, we investigate consequent initial value problems by using the theory of reproducing kernels. A new method is proposed which -- in particular -- generates a new field among initial value problems, linear integral operators, eigenfunctions and values, integral transforms and reproducing kernels. In particular, examples are worked out for the integral equations ...
A Bessel differential heat initial value problem in a reproducing kernel Hilber...
Castro, L.P.; Rodrigues, M.M.; Saitoh, S.For modified Bessel heat equations subjected to an initial condition, we investigate integral transforms with kernels related to the solutions of those equations by using the theory of reproducing kernels. In particular, a new framework within reproducing kernel Hilbert spaces is proposed where we construct the unique solutions of the corresponding initial value problems.