Fractional Integrals and Derivatives: "True" versus "False"

• Other Authors: Luchko, Yuri (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021
• Subjects: Research & information: general; Mathematics & science; fractional derivatives; fractional integrals; fractional calculus; fractional anti-derivatives; fractional operators; integral transforms; convergent series; fractional integral; fractional derivative; numerical approximation; translation operator; distributed lag; time delay; scaling; dilation; memory; depreciation; probability distribution; fractional models; fractional differentiation; distributed time delay systems; Volterra equation; adsorption; fractional differential equations; numerical methods; smoothness assumptions; persistent memory; initial values; existence; uniqueness; Crank-Nicolson scheme; weighted Shifted Grünwald-Letnikov approximation; space fractional convection-diffusion model; stability analysis; convergence order; Caputo-Fabrizio operator; Atangana-Baleanu operator; fractional falculus; general fractional derivative; general fractional integral; Sonine condition; fractional relaxation equation; fractional diffusion equation; Cauchy problem; initial-boundary-value problem; inverse problem; fractional calculus operators; special functions; generalized hypergeometric functions; integral transforms of special functions
• Online Access: DOAB: download the publication; DOAB: description of the publication

This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like "What are the fractional integrals and derivatives?", "What are their decisive mathematical properties?",...