Advances in Fractional Differential Operators and Their Applications

doi:10.3390/books978-3-0365-8905-3

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Advances in Fractional Differential Operators and Their Applications

Edited by

October 2023

374 pages

ISBN978-3-0365-8904-6 (Hardback)
ISBN978-3-0365-8905-3 (PDF)

https://doi.org/10.3390/books978-3-0365-8905-3

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This book is a reprint of the Special Issue Advances in Fractional Differential Operators and Their Applications that was published in

Computer Science & Mathematics

Summary

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.

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Keywords

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; fractional calculus; Laplace transform; Mittag-Leffler function; eigenvalues; asymptotics; Cahn–Hilliard equation; fractional Laplacian; memory; two dimensional Volterra integral equation; operational matrix; block pulse; operational matrix; 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; Laplace transform; 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; fractional differential equations; 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; approximate solution; partial differential equation; Riemann–Liouville derivatives; 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; fractional differential equations; Lotka–Volterra system; boundedness; stability; fractional piecewise order derivative; variable kernel; existence of solution; stability results; time series; sequence operator; fractional-order operator; model stability; model perturbation analysis