Choose an application

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

This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

mathematical economics --- economic theory --- fractional calculus --- fractional dynamics --- long memory --- non-locality --- fractional generalization --- econometric modelling --- identification --- Phillips curve --- Mittag-Leffler function --- generalized fractional derivatives --- growth equation --- Mittag–Leffler function --- Caputo fractional derivative --- economic growth model --- least squares method --- fractional diffusion equation --- fundamental solution --- option pricing --- risk sensitivities --- portfolio hedging --- business cycle model --- stability --- time delay --- time-fractional-order --- Hopf bifurcation --- Einstein’s evolution equation --- Kolmogorov–Feller equation --- diffusion equation --- self-affine stochastic fields --- random market hypothesis --- efficient market hypothesis --- fractal market hypothesis --- financial time series analysis --- evolutionary computing --- modelling --- economic growth --- prediction --- Group of Twenty --- pseudo-phase space --- economy --- system modeling --- deep assessment --- least squares --- modeling --- GDP per capita --- LSTM --- econophysics --- continuous-time random walk (CTRW) --- Mittag–Leffler functions --- Laplace transform --- Fourier transform --- n/a --- Einstein's evolution equation --- Kolmogorov-Feller equation --- Mittag-Leffler functions

Choose an application

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

This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.

fractional derivatives --- fractional integrals --- fractional calculus --- fractional anti-derivatives --- fractional operators --- integral transforms --- convergent series --- fractional integral --- fractional derivative --- numerical approximation --- translation operator --- distributed lag --- time delay --- scaling --- dilation --- memory --- depreciation --- probability distribution --- fractional models --- fractional differentiation --- distributed time delay systems --- Volterra equation --- adsorption --- fractional differential equations --- numerical methods --- smoothness assumptions --- persistent memory --- initial values --- existence --- uniqueness --- Crank–Nicolson scheme --- weighted Shifted Grünwald–Letnikov approximation --- space fractional convection-diffusion model --- stability analysis --- convergence order --- Caputo–Fabrizio operator --- Atangana–Baleanu operator --- fractional falculus --- general fractional derivative --- general fractional integral --- Sonine condition --- fractional relaxation equation --- fractional diffusion equation --- Cauchy problem --- initial-boundary-value problem --- inverse problem --- fractional calculus operators --- special functions --- generalized hypergeometric functions --- integral transforms of special functions

Choose an application

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

This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

Economics, finance, business & management --- mathematical economics --- economic theory --- fractional calculus --- fractional dynamics --- long memory --- non-locality --- fractional generalization --- econometric modelling --- identification --- Phillips curve --- Mittag-Leffler function --- generalized fractional derivatives --- growth equation --- Caputo fractional derivative --- economic growth model --- least squares method --- fractional diffusion equation --- fundamental solution --- option pricing --- risk sensitivities --- portfolio hedging --- business cycle model --- stability --- time delay --- time-fractional-order --- Hopf bifurcation --- Einstein's evolution equation --- Kolmogorov-Feller equation --- diffusion equation --- self-affine stochastic fields --- random market hypothesis --- efficient market hypothesis --- fractal market hypothesis --- financial time series analysis --- evolutionary computing --- modelling --- economic growth --- prediction --- Group of Twenty --- pseudo-phase space --- economy --- system modeling --- deep assessment --- least squares --- modeling --- GDP per capita --- LSTM --- econophysics --- continuous-time random walk (CTRW) --- Mittag-Leffler functions --- Laplace transform --- Fourier transform

Choose an application

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

Unconventional reservoirs are usually complex and highly heterogeneous, such as shale, coal, and tight sandstone reservoirs. The strong physical and chemical interactions between fluids and pore surfaces lead to the inapplicability of conventional approaches for characterizing fluid flow in these low-porosity and ultralow-permeability reservoir systems. Therefore, new theories and techniques are urgently needed to characterize petrophysical properties, fluid transport, and their relationships at multiple scales for improving production efficiency from unconventional reservoirs. This book presents fundamental innovations gathered from 21 recent works on novel applications of new techniques and theories in unconventional reservoirs, covering the fields of petrophysical characterization, hydraulic fracturing, fluid transport physics, enhanced oil recovery, and geothermal energy. Clearly, the research covered in this book is helpful to understand and master the latest techniques and theories for unconventional reservoirs, which have important practical significance for the economic and effective development of unconventional oil and gas resources.

shale gas --- permeability --- prediction by NMR logs --- matrix–fracture interaction --- faults --- remaining oil distributions --- unconventional reservoirs --- coal deformation --- reservoir depletion --- carbonate reservoir --- nanopore --- fracturing fluid --- pseudo-potential model --- shale reservoirs --- matrix-fracture interactions --- multi-scale fracture --- succession pseudo-steady state (SPSS) method --- fluid transport physics --- integrated methods --- chelating agent --- dissolved gas --- non-equilibrium permeability --- effective stress --- fractal --- fracture network --- spontaneous imbibition --- tight oil --- porous media --- 0-1 programming --- the average flow velocity --- geothermal water --- micro-fracture --- pore types --- pore network model --- petrophysical characterization --- nitrogen adsorption --- analysis of influencing factors --- mudstone --- rheology --- velocity profile --- shale permeability --- flow resistance --- global effect --- tight sandstones --- fractal dimension --- contact angle --- temperature-resistance --- fractured well transient productivity --- reservoir classifications --- deep circulation groundwater --- viscosity --- NMR --- fractional diffusion --- lattice Boltzmann method --- multiporosity and multiscale --- fractal geometry --- imbibition front --- productivity contribution degree of multimedium --- wetting angle --- pH of formation water --- enhanced oil recovery --- isotopes --- tight sandstone --- fracture diversion --- shale --- SRV-fractured horizontal well --- low-salinity water flooding --- shale gas reservoir --- tight reservoirs --- fracture continuum method --- tight oil reservoir --- Lucaogou Formation --- hydraulic fracturing --- clean fracturing fluid --- recovery factor --- flow regimes --- local effect --- complex fracture network --- pore structure --- gas adsorption capacity --- polymer --- non-linear flow --- conformable derivative --- production simulation --- analytical model --- enhanced geothermal system --- multi-scale flow --- experimental evaluation --- extended finite element method --- fluid-solid interaction --- groundwater flow --- well-placement optimization --- thickener --- imbibition recovery --- equilibrium permeability --- slip length --- large density ratio --- clay mineral composition --- finite volume method --- volume fracturing --- influential factors --- sulfonate gemini surfactant

Choose an application

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

It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.

Research & information: general --- Mathematics & science --- dynamic equations --- time scales --- classification --- existence --- necessary and sufficient conditions --- fractional calculus --- triangular fuzzy number --- double-parametric form --- FRDTM --- fractional dynamical model of marriage --- approximate controllability --- degenerate evolution equation --- fractional Caputo derivative --- sectorial operator --- fractional symmetric Hahn integral --- fractional symmetric Hahn difference operator --- Arrhenius activation energy --- rotating disk --- Darcy–Forchheimer flow --- binary chemical reaction --- nanoparticles --- numerical solution --- fractional differential equations --- two-dimensional wavelets --- finite differences --- fractional diffusion-wave equation --- fractional derivative --- ill-posed problem --- Tikhonov regularization method --- non-linear differential equation --- cubic B-spline --- central finite difference approximations --- absolute errors --- second order differential equations --- mild solution --- non-instantaneous impulses --- Kuratowski measure of noncompactness --- Darbo fixed point --- multi-stage method --- multi-step method --- Runge–Kutta method --- backward difference formula --- stiff system --- numerical solutions --- Riemann-Liouville fractional integral --- Caputo fractional derivative --- fractional Taylor vector --- kerosene oil-based fluid --- stagnation point --- carbon nanotubes --- variable thicker surface --- thermal radiation --- differential equations --- symmetric identities --- degenerate Hermite polynomials --- complex zeros --- oscillation --- third order --- mixed neutral differential equations --- powers of stochastic Gompertz diffusion models --- powers of stochastic lognormal diffusion models --- estimation in diffusion process --- stationary distribution and ergodicity --- trend function --- application to simulated data --- n-th order linear differential equation --- two-point boundary value problem --- Green function --- linear differential equation --- exponential stability --- linear output feedback --- stabilization --- uncertain system --- nonlocal effects --- linear control system --- Hilbert space --- state feedback control --- exact controllability --- upper Bohl exponent