Fractional-Order Integral and Derivative Operators and Their Applications

• Format: eBook
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: Mathematics and Science; Research and information: general; analytic functions; Appell's functions; approximate solution; available potassium; Banach space; cardioid domain; close-to-convex functions; collocation points; confluent hypergeometric function; conic and generalized conic domains; conic domains; controllability; convergence analysis; convex functions; correlation analysis; coupled system; desert soil; differential subordination; error analysis; field spectrum; fractional calculus; fractional derivatives; fractional differential equations; fractional differential systems; fractional diffusion equation; fractional in time and space shallow-water system; fractional integrals; fractional order model; fractional order Takagi-Sugeno models; fractional order unknown input fuzzy observer; Gauss hypergeometric function; generating functions; global solutions; Hadamard derivative; Hankel determinant; Hermite collocation method; Hermite polynomials and series; Hilfer derivative; Hilfer fractional derivative; HIV infection; impulsive system; incomplete fractional calculus; initial value problem; Janowski function; L2 optimization; Laplace operators; latent reservoir; Legendre wavelet; length problems; limacon domain; linear matrix inequalities; Liouville_Caputo sense; logarithm; logarithmic coefficients; Mittag-Leffler functions; Miura transform; mixed Hadamard integral; mixed Riemann-Liouville integral; monotone iterative method; multivalent functions; n/a; non-linear fractional variational problems; nonlocal boundary conditions; nonlocal integral condition; operational matrix; orthogonal polynomials; pantograph differential equation; piecewise constant functions; Post-Exposure Prophylaxis; q-calculus; q-derivative operator; q-hypergeometric functions; random solution; Rayleigh-Ritz method; Riemann-Liouville fractional integral; Riemann-stieltjes integral; sine function; SIR model; Sobolev space; soliton equations; starlike and q-starlike functions; starlike function; starlike functions; subordination; systems of fractional order differential equations; Toeplitz determinant; Toeplitz matrices; Ulam stability; uniformly close-to-convex functions; uniformly starlike functions; unique continuation property; univalent functions; unmeasurable premise variables; upper and lower solutions; upper bound; variable order fractional derivative; ψ-Caputo fractional derivative
• Online Access: Open Access: DOAB: description of the publication; Open Access: DOAB, download the publication

 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.