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During the past four decades or so, various operators of fractional calculus, 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 popular and important due mainly to their demonstrated applications in numerous diverse and widespread fields of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional calculus operators provide several potentially useful tools for solving differential, integral, differintegral, and integrodifferential equations, together with the fractionalcalculus analogues and extensions of each of these equations, and various other problems involving special functions of mathematical physics, as well as their extensions and generalizations in one and more variables. In this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional calculus and its multidisciplinary applications.
operators of fractional calculus  chaos and fractional dynamics  fractional differential  fractional differintegral equations  fractional integrodifferential equations  fractional integrals  fractional derivatives associated with special functions of mathematical physics  applied mathematics  identities and inequalities involving fractional integrals  fractional derivatives
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Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.
analytic functions  starlike functions  convex functions  FeketeSzegö inequality  Hilbert C*module  gframe  gBessel sequence  adjointable operator  analytic functions  starlike functions  convex functions  FeketeSzegö inequality  operator inequality  positive linear map  operator Kantorovich inequality  geometrically convex function  frame  weaving frame  weaving frame operator  alternate dual frame  Hilbert space  quantum estimates  HermiteHadamard type inequalities  quasiconvex  Hermite–Hadamard type inequality  strongly ?convex functions  Hölder’s inequality  Power mean inequality  Katugampola fractional integrals  Riemann–Liouville fractional integrals  Hadamard fractional integrals  Steffensen’s inequality  higher order convexity  Green functions  Montgomery identity  Fink’s identity  HermiteHadamard inequality  intervalvalued functions  (h1, h2)convex  majorization inequality  twice differentiable convex functions  refined inequality  Taylor theorem  Gronwall–Bellman inequality  proportional fractional derivative  Riemann–Liouville and Caputo proportional fractional initial value problem  convex functions  Fejér’s inequality  special means  weaving frame  weaving Kframe  Kdual  pseudoinverse  ?variation  onesided singular integral  commutator  onesided weighted Morrey space  onesided weighted Campanato space  power inequalities  exponential inequalities  trigonometric inequalities  weight function  halfdiscrete HardyHilbert’s inequality  parameter  EulerMaclaurin summation formula  reverse inequality
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