Advances in Fractional Differential Operators and Their Applications

• Other Authors: Mingarelli, Angelo B. (Editor), Zivlaei, Leila Gholizadeh (Editor), Dehghan, Mohammad (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: Research & information: general; Mathematics & science; Mellin-Barnes integrals; Sinc methods; Sinc quadrature; Fox functions; Aleph functions; Saxena function; definite integrals; fractional calculus; fractional Langevin equation; ML-kernel; existence of solutions; UH-type stability; numerical simulation; Caputo sense; space-fractional Fisher's equation; cubic polynomial spline; von Neumann stability; fractional differential equations; κ(x)-Laplacian; χ-Hilfer fractional derivative; existence; multiplicity of solutions; genus theory; Concentration-Compactness Principle; Mountain Pass Theorem; variable exponents; variational methods; Fractional Sturm-Liouville; Laplace transform; Mittag-Leffler function; eigenvalues; asymptotics; Cahn-Hilliard equation; fractional Laplacian; memory; two dimensional Volterra integral equation; operational matrix; block pulse; Taylor polynomials; gradient nonlinearity; fractional diffusion equation; hyper-Bessel; fractional partial differential equations; fractional differential equation; p-derivative; power-law visco-elasto-plasticity; time-fractional integration; fractional quasi-linear viscoelasticity; fractional Riccati differential equation; approximate solution; residual power series; fractional wave equation; Riemann-Liouville derivatives; inverse problem; determination of the order of derivative; Fourier method; evolution equations; operator function; Abel-Lidskii basis property; Schatten-von Neumann class; multi-order fractional differential equation; stability; instability; Caputo derivative; cantilever beam; existence and uniqueness of minimizers; fractional boundary value problem; Euler-Lagrange theorem; homotopy perturbation method; fractional Fornberg-Whitham equation; partial differential equation; Caputo's derivatives; variational iteration method; Adomian decomposition method; homotopy analysis method; fractional-order nonlinear system; Razumikhin approach; input delay; distributed delay; leader-following consensus; Lotka-Volterra system; boundedness; fractional piecewise order derivative; variable kernel; existence of solution; stability results; time series; sequence operator; fractional-order operator; model stability; model perturbation analysis
• Online Access: DOAB: download the publication; DOAB: description of 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, dist...