Reprint

# Fractional-Order Integral and Derivative Operators and Their Applications

Edited by

August 2020

344 pages

- ISBN978-3-03936-650-7 (Hardback)
- ISBN978-3-03936-651-4 (PDF)

This book is a reprint of the Special Issue Fractional-Order Integral and Derivative Operators and Their Applications that was published in

Computer Science & Mathematics

Engineering

Physical Sciences

Public Health & Healthcare

Summary

In recent years, various families of fractional-order integral and derivative operators, such as those named after Riemann-Liouville, Weyl, Hadamard, Grunwald-Letnikov, Riesz, Erdelyi-Kober, Liouville-Caputo, and so on, have been found to be remarkably important and fruitful, due mainly to their demonstrated applications in numerous seemingly diverse and widespread areas of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional-order operators provide interesting, potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables. For this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional-order integral and derivative operators and their multidisciplinary applications.

Format

- Hardback

License

© 2020 by the authors; CC BY-NC-ND license

Keywords

Legendre wavelet; operational matrix; systems of fractional order differential equations; Liouville_Caputo sense; analytic functions; starlike functions; univalent functions; length problems; SIR model; Hermite collocation method; approximate solution; Hermite polynomials and series; collocation points; analytic functions; starlike and

*q*-starlike functions;*q*-derivative operator;*q*-hypergeometric functions; conic and generalized conic domains; Hankel determinant; Toeplitz matrices; fractional differential equations; Riemann-stieltjes integral; monotone iterative method; upper and lower solutions; fractional diffusion equation; controllability; impulsive system; unique continuation property; non-linear fractional variational problems; orthogonal polynomials; Rayleigh-Ritz method; error analysis; convergence analysis; Banach space; Sobolev space; Laplace operators; nonlocal boundary conditions; fractional differential systems; mixed Riemann–Liouville integral; mixed Hadamard integral; Hilfer derivative; Hadamard derivative; coupled system; random solution; variable order fractional derivative; initial value problem; fractional differential equations; piecewise constant functions; approximate solution; starlike function; Toeplitz determinant; Hankel determinant; sine function; upper bound; starlike functions; convex functions; subordination; logarithmic coefficients; Gauss hypergeometric function; confluent hypergeometric function; Appell’s functions; incomplete fractional calculus; Riemann-Liouville fractional integral; generating functions; fractional integrals; fractional derivatives; Mittag–Leffler functions; field spectrum; fractional calculus; desert soil; available potassium; correlation analysis; Post-Exposure Prophylaxis; latent reservoir; HIV infection; fractional order model; analytic functions; multivalent functions; starlike functions; close-to-convex functions; uniformly starlike functions; uniformly close-to-convex functions; conic domains;*q*-calculus; differential subordination; Janowski function; cardioid domain; limacon domain; fractional order unknown input fuzzy observer; fractional order Takagi–Sugeno models;*L*optimization; linear matrix inequalities; unmeasurable premise variables; global solutions; fractional in time and space shallow-water system;_{2}*ψ*-Caputo fractional derivative; Hilfer fractional derivative; Ulam stability; pantograph differential equation; nonlocal integral condition; Miura transform; soliton equations; logarithm; n/a