Advances in Fractional Differential Operators and Their Applications

• Format: eBook
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: 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
• DOI: 10.3390/books978-3-0365-8905-3

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.