Advances in Fractional Differential Operators and Their Applications

The application of generalized and fractional derivatives, such as Caputo and Riemann–Liouville derivatives, has witnessed a dramatic increase in recent years. This reprint focuses on related theoretical and applied research in areas such as the stability of time series, Lotka–Volterra systems, dist...

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Médium:	E-kniha
Jazyk:	angličtina
Vydáno:	Basel MDPI - Multidisciplinary Digital Publishing Institute 2023
Témata:	Abel–Lidskii basis property Adomian decomposition method Aleph functions approximate solution asymptotics block pulse boundedness Cahn–Hilliard equation cantilever beam Caputo derivative Caputo sense Caputo’s derivatives Concentration-Compactness Principle cubic polynomial spline definite integrals determination of the order of derivative distributed delay eigenvalues Euler–Lagrange theorem evolution equations existence existence and uniqueness of minimizers existence of solution existence of solutions Fourier method Fox functions fractional boundary value problem fractional calculus fractional differential equation fractional differential equations fractional diffusion equation fractional Fornberg–Whitham equation fractional Langevin equation fractional Laplacian fractional partial differential equations fractional piecewise order derivative fractional quasi-linear viscoelasticity fractional Riccati differential equation Fractional Sturm–Liouville fractional wave equation fractional-order nonlinear system fractional-order operator genus theory gradient nonlinearity homotopy analysis method homotopy perturbation method hyper-Bessel input delay instability inverse problem Laplace transform leader–following consensus Lotka–Volterra system Mathematics and Science Mellin-Barnes integrals memory Mittag-Leffler function ML-kernel model perturbation analysis model stability Mountain Pass Theorem multi-order fractional differential equation multiplicity of solutions numerical simulation operational matrix operator function p-derivative partial differential equation power-law visco-elasto-plasticity Razumikhin approach Reference, Information and Interdisciplinary subjects Research and information: general residual power series Riemann–Liouville derivatives Saxena function Schatten–von Neumann class sequence operator Sinc methods Sinc quadrature space-fractional Fisher’s equation stability stability results Taylor polynomials time series time-fractional integration two dimensional Volterra integral equation UH-type stability variable exponents variable kernel variational iteration method variational methods von Neumann stability κ(x)-Laplacian χ-Hilfer fractional derivative
ISBN:	9783036589053, 303658904X, 3036589058, 9783036589046
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Shrnutí:	The application of generalized and fractional derivatives, such as Caputo and Riemann–Liouville derivatives, has witnessed a dramatic increase in recent years. This reprint focuses on related theoretical and applied research in areas such as the stability of time series, Lotka–Volterra systems, distributed delays, Fornberg–Whitham equations, abstract evolution and fractional wave equations, cantilever beams, and fractional Riccati and Volterra equations, as well as fractional visco-elasto-plasticity, spectral theory for fractional Sturm–Liouville problems, generalized differential equations, Mittag–Leffler functions, and fractional Laplacians.
ISBN:	9783036589053 303658904X 3036589058 9783036589046
DOI:	10.3390/books978-3-0365-8905-3