Fractional-Order Integral and Derivative Operators and Their Applications

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...

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Other Authors:	Srivastava, Hari Mohan (Editor)
Format:	Book Chapter
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
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Fractional-Order Integral and Derivative Operators and Their Applications

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