Fractional-Order Integral and Derivative Operators and Their Applications

• Other Authors: Srivastava, Hari Mohan (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: Research & information: general; Mathematics & science; 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; 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; piecewise constant functions; starlike function; Toeplitz determinant; sine function; upper bound; 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; multivalent 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; L2 optimization; linear matrix inequalities; unmeasurable premise variables; global solutions; fractional in time and space shallow-water system; ψ-Caputo fractional derivative; Hilfer fractional derivative; Ulam stability; pantograph differential equation; nonlocal integral condition; Miura transform; soliton equations; logarithm; n/a
• Online Access: DOAB: download the publication; DOAB: description of 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 dem...