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Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem.

Technology: general issues --- fractional kinetic equation --- Riemann–Liouville fractional integral operator --- incomplete I-functions --- Laplace transform --- fractional differential equations --- fractional generalized biologic population --- Sumudu transform --- Adomian decomposition method --- Caputo fractional derivative --- operator theory --- time scales --- integral inequalities --- Burgers’ equation --- reproducing kernel method --- error estimate --- Dirichlet and Neumann boundary conditions --- Caputo derivative --- Laplace transforms --- constant proportional Caputo derivative --- modeling --- Volterra-type fractional integro-differential equation --- Hilfer fractional derivative --- Lorenzo-Hartely function --- generalized Lauricella confluent hypergeometric function --- Elazki transform --- caputo fractional derivative --- predator–prey model --- harvesting rate --- stability analysis --- equilibrium point --- implicit discretization numerical scheme --- the (m + 1/G′)-expansion method --- the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation --- periodic and singular complex wave solutions --- traveling waves solutions --- chaotic finance --- fractional calculus --- Atangana-Baleanu derivative --- uniqueness of the solution --- fixed point theory --- shifted Legendre polynomials --- variable coefficient --- three-point boundary value problem --- modified alpha equation --- Bernoulli sub-equation function method --- rational function solution --- complex solution --- contour surface --- variable exponent --- fractional integral --- maximal operator --- n/a --- Riemann-Liouville fractional integral operator --- Burgers' equation --- predator-prey model --- the (m + 1/G')-expansion method --- the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation

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This book offers a collection of 30 scientific papers which address the problems associated with the use of power electronic converters in renewable energy source-based systems. Relevant problems associated with the use of power electronic converters to integrate renewable energy systems to the power grid are presented. Some of the covered topics relate to the integration of photovoltaic and wind energy generators into the rest of the system, and to the use of energy storage to mitigate power fluctuations, which are a characteristic of renewable energy systems. The book provides a good overview of the abovementioned topics.

n/a --- washout filter --- turbine and generator --- unbalanced power grid --- PV --- transient dynamics --- multi-input single output (MISO) --- permanent magnet synchronous generator (PMSG) --- static frequency characteristics --- impedance analysis --- FACTS devices --- coordinated control --- improved additional frequency control --- experiment --- resonant controller --- two-stage photovoltaic power --- voltage cancellation --- energy --- power matching --- LCL filter --- adaptive-MPPT (maximum power point tracking) --- VSC --- active power filter --- perturb and observe --- coordination control --- voltage-type control --- multiple VSGs --- wind power prediction --- linear quadratic regulator --- multiport converter (MPC) --- grid support function --- power ripple elimination --- adaptive resonant controller --- phase space reconstruction --- sliding mode control --- impedance emulation --- photovoltaic systems --- grid-connected converter --- SVM --- photovoltaic generators --- power grid --- active front-end converter --- THD --- type-4 wind turbine --- inertia --- ROCOF --- microgrid --- coupled oscillators --- multilevel power converter --- DC-AC power converters --- internal model --- back-to-back converter --- duty-ratio constraints --- selective harmonic mitigation --- parallel inverters --- discontinuous conduction mode --- droop control --- step size --- grid-connected --- inverter --- short-circuit fault --- energy router --- oscillation mitigation --- improved-VSG (virtual synchronous generator) --- source and load impedance --- synchronverter --- digital signal processor (DSP) TMS320F28335 --- operation optimization --- battery-energy storage --- generator speed control --- electrical power generation --- virtual impedance --- weak grid --- doubly-fed induction generator --- grid synchronization --- Energy Internet --- open circuit voltage --- state-of-charge balancing --- renewable power system --- control strategies --- adaptive notch filter (ANF) --- renewable energy --- hardware in the loop (HIL) --- energy storage --- microgrids --- inertia and damping characteristics --- electric vehicle --- multi-energy complementary --- static compensator --- stability --- battery energy storage system --- power-hardware-in- the-loop --- electricity price --- notch filter --- time series --- distorted grid --- oscillation suppression --- phase-locked loop (PLL) --- modules --- organic Rankine cycle --- failure zone --- Opal-RT Technologies® --- distributed generation --- modular multilevel converter --- governor --- microgrid (MG) --- second-life battery --- thermoelectric generator --- stability analysis --- wind energy system --- variable coefficient regulation --- single ended primary inductor converter (SEPIC) --- error --- soft switching --- power electronics --- PLL --- SPWM --- virtual synchronous generator --- perturbation frequency --- phase shifted --- grid-connected inverter --- cloud computing --- low inertia --- boost converter --- impedance reshaping --- small-signal and transient stability --- speed control --- multivariate linear regression --- photovoltaic --- adaptive control --- frequency regulation --- variable power tracking control --- power converters --- maximum power point tracking --- virtual admittance --- synchronization --- peak-current-mode control --- dynamic modeling --- discontinuous operation mode --- demand response