New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus

doi:10.3390/books978-3-0365-4906-4

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New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus

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August 2022

368 pages

ISBN978-3-0365-4905-7 (Hardback)
ISBN978-3-0365-4906-4 (PDF)

https://doi.org/10.3390/books978-3-0365-4906-4

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This book is a reprint of the Special Issue New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus that was published in

Computer Science & Mathematics

Summary

This reprint focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems.

It is impossible to deny that fractional behaviour exists in nature. Any phenomenon that has a pulse, rhythm, or pattern appears to be a fractal. The 17 papers that were published and are part of this volume provide credence to that claim. A variety of topics illustrate the use of fractional calculus in a range of disciplines and offer sufficient coverage to pique every reader's attention.

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Keywords

bessel function; harmonically convex function; non-singular function involving kernel fractional operator; harmonically convex function; Hadamard inequality; Fejér–Hadamard inequality; Elzaki transform; Caputo fractional derivative; AB-fractional operator; new iterative transform method; Fisher’s equation; Elzaki transform; Hukuhara difference; Caputo fractional derivative; Atangana–Baleanu fractional derivative operator; Mittag–Leffler kernel; Fornberg–Whitham equation; fractional div-curl systems; Helmholtz decomposition theorem; Riemann–Liouville derivative; Caputo derivative; fractional vector operators; weighted (k,s) fractional integral operator; weighted (k,s) fractional derivative; weighted generalized Laplace transform; fractional kinetic equation; typhoid fever disease; vaccination; model calibration; Caputo derivative; asymptotic stability; fixed point theory; nonlinear models; efficiency index; computational cost; Halley’s method; basin of attraction; computational order of convergence; Caputo–Hadamard fractional derivative; thermostat modeling; Caputo–Hadamard fractional integral; hybrid Caputo–Hadamard fractional differential equation and inclusion; prey-predator model; boundedness; period-doubling bifurcation; Neimark-Sacker bifurcation; hybrid control; fractal dimensions; cubic B-splines; trigonometric cubic B-splines; extended cubic B-splines; Caputo–Fabrizio derivative; Cattaneo equation; Hermite-Hadamard-type inequalities; Hilfer fractional derivative; Hölder’s inequality; fractional-order differential equations; operational matrices; shifted Vieta–Lucas polynomials; Caputo derivative; Adomian decomposition method; system of Whitham-Broer-Kaup equations; Caputo-Fabrizio derivative; Yang transform; ϑ-Caputo derivative; extremal solutions; monotone iterative method; sequences; convex; exponential convex; fractional; quantum; inequalities; Gould-Hopper-Laguerre-Sheffer matrix polynomials; quasi-monomiality; umbral calculus; fractional calculus; Euler’s integral of gamma functions; beta function; generalized hypergeometric series; operational methods; delta function; Riemann zeta-function; fractional transforms; Fox–Wright-function; generalized fractional kinetic equation; n/a