Fractional Calculus - Theory and Applications

doi:10.3390/books978-3-0365-3263-9

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Fractional Calculus - Theory and Applications

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June 2022

198 pages

ISBN978-3-0365-3262-2 (Hardback)
ISBN978-3-0365-3263-9 (PDF)

https://doi.org/10.3390/books978-3-0365-3263-9

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This book is a reprint of the Special Issue Fractional Calculus - Theory and Applications that was published in

Computer Science & Mathematics

Physical Sciences

Summary

In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications.

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Keywords

Caputo fractional derivative; fractional differential equations; hybrid differential equations; coupled hybrid Sturm–Liouville differential equation; multi-point boundary coupled hybrid condition; integral boundary coupled hybrid condition; dhage type fixed point theorem; Caputo fractional derivative; linear fractional system; distributed delay; finite time stability; impulsive differential equations; fractional impulsive differential equations; instantaneous impulses; non-instantaneous impulses; time-fractional diffusion-wave equations; Euler wavelets; integral equations; numerical approximation; coupled systems; Riemann–Liouville fractional derivative; Hadamard–Caputo fractional derivative; nonlocal boundary conditions; existence; fixed point; LR-p-convex interval-valued function; Katugampola fractional integral operator; Hermite-Hadamard type inequality; Hermite-Hadamard-Fejér inequality; space–fractional Fokker–Planck operator; time–fractional wave with the time–fractional damped term; Laplace transform; Mittag–Leffler function; Grünwald–Letnikov scheme; potential and current in an electric transmission line; random walk of a population; fractional derivative; gradient descent; economic growth; group of seven; fractional order derivative model; GPU; a spiral-plate heat exchanger; parallel model; heat transfer; nonlinear system; stochastic epidemic model; malaria infection; stochastic generalized Euler; nonstandard finite-difference method; positivity; boundedness; n/a