Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In recent years, various families of fractional-order integral and derivative operators, such as those named after Riemann-Liouville, Weyl, Hadamard, Grunwald-Letnikov, Riesz, Erdelyi-Kober, Liouville-Caputo, and so on, have been found to be remarkably important and fruitful, due mainly to their demonstrated applications in numerous seemingly diverse and widespread areas of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional-order operators provide interesting, potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables. For this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional-order integral and derivative operators and their multidisciplinary applications.

Legendre wavelet --- operational matrix --- systems of fractional order differential equations --- Liouville_Caputo sense --- analytic functions --- starlike functions --- univalent functions --- length problems --- SIR model --- Hermite collocation method --- approximate solution --- Hermite polynomials and series --- collocation points --- starlike and q-starlike functions --- q-derivative operator --- q-hypergeometric functions --- conic and generalized conic domains --- Hankel determinant --- Toeplitz matrices --- fractional differential equations --- Riemann-stieltjes integral --- monotone iterative method --- upper and lower solutions --- fractional diffusion equation --- controllability --- impulsive system --- unique continuation property --- non-linear fractional variational problems --- orthogonal polynomials --- Rayleigh-Ritz method --- error analysis --- convergence analysis --- Banach space --- Sobolev space --- Laplace operators --- nonlocal boundary conditions --- fractional differential systems --- mixed Riemann–Liouville integral --- mixed Hadamard integral --- Hilfer derivative --- Hadamard derivative --- coupled system --- random solution --- variable order fractional derivative --- initial value problem --- piecewise constant functions --- starlike function --- Toeplitz determinant --- sine function --- upper bound --- convex functions --- subordination --- logarithmic coefficients --- Gauss hypergeometric function --- confluent hypergeometric function --- Appell’s functions --- incomplete fractional calculus --- Riemann-Liouville fractional integral --- generating functions --- fractional integrals --- fractional derivatives --- Mittag–Leffler functions --- field spectrum --- fractional calculus --- desert soil --- available potassium --- correlation analysis --- Post-Exposure Prophylaxis --- latent reservoir --- HIV infection --- fractional order model --- multivalent functions --- close-to-convex functions --- uniformly starlike functions --- uniformly close-to-convex functions --- conic domains --- q-calculus --- differential subordination --- Janowski function --- cardioid domain --- limacon domain --- fractional order unknown input fuzzy observer --- fractional order Takagi–Sugeno models --- L2 optimization --- linear matrix inequalities --- unmeasurable premise variables --- global solutions --- fractional in time and space shallow-water system --- ψ-Caputo fractional derivative --- Hilfer fractional derivative --- Ulam stability --- pantograph differential equation --- nonlocal integral condition --- Miura transform --- soliton equations --- logarithm --- n/a --- mixed Riemann-Liouville integral --- Appell's functions --- Mittag-Leffler functions --- fractional order Takagi-Sugeno models

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Mesoscopic physics deals with systems larger than single atoms but small enough to retain their quantum properties. The possibility to create and manipulate conductors of the nanometer scale has given birth to a set of phenomena that have revolutionized physics: quantum Hall effects, persistent currents, weak localization, Coulomb blockade, etc. This Special Issue tackles the latest developments in the field. Contributors discuss time-dependent transport, quantum pumping, nanoscale heat engines and motors, molecular junctions, electron–electron correlations in confined systems, quantum thermo-electrics and current fluctuations. The works included herein represent an up-to-date account of exciting research with a broad impact in both fundamental and applied topics.

quantum transport --- quantum interference --- shot noise --- persistent current --- mesoscale and nanoscale physics --- Complementary Metal Oxide Semiconductor (CMOS) technology --- electron quantum optics --- photo-assisted noise --- charge and heat fluctuations --- time-dependent transport --- electron–photon coupling --- open quantum systems --- phonon transport --- nanostructured materials --- green’s functions --- density-functional tight binding --- Landauer approach, time-dependent transport --- graphene nanoribbons --- nonequilibrium Green’s function --- electronic transport --- thermal transport --- strongly correlated systems --- Landauer-Büttiker formalism --- Boltzmann transport equation --- time-dependent density functional theory --- electron–phonon coupling --- molecular junctions --- thermoelectric properties --- electron–vibration interactions --- electron–electron interactions --- thermoelectricity --- heat engines --- mesoscopic physics --- fluctuations --- thermodynamic uncertainty relations --- quantum thermodynamics --- steady-state dynamics --- nonlinear transport --- adiabatic quantum motors --- adiabatic quantum pumps --- quantum heat engines --- quantum refrigerators --- transport through quantum dots --- spin pump --- spin-orbit interaction --- quantum adiabatic pump --- interferometer --- geometric phase --- nonadiabaticity --- quantum heat pumping --- spin pumping --- relaxation --- time evolution --- quantum information --- entropy production --- Renyi entropy --- superconducting proximity effect --- Kondo effect --- spin polarization --- Anreev reflection --- conditional states --- conditional wavefunction --- Markovian and Non-Markovian dynamics --- stochastic Schrödinger equation --- quantum electron transport --- quantum dots --- fluctuation–dissipation theorem --- Onsager relations --- dynamics of strongly correlated quantum systems --- quantum capacitor --- local fermi liquids --- kondo effect --- coulomb blockade --- mesoscopic systems --- nanophysics --- quantum noise --- quantum pumping --- thermoelectrics --- heat transport