Advances in Fractional Differential Operators and Their Applications

• Format: eBook
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: Mathematics & science; Research & information: general; 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; 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; 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
• Online Access: Open Access: DOAB: description of the publication; Open Access: DOAB, download the publication

 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.