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

• Other Authors: Tassaddiq, Asifa (Editor), Yaseen, Muhammad (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel 2022
• Subjects: Research & information: general; Mathematics & science; bessel function; harmonically convex function; non-singular function involving kernel fractional operator; Hadamard inequality; Fejér-Hadamard inequality; Elzaki transform; Caputo fractional derivative; AB-fractional operator; new iterative transform method; Fisher's equation; Hukuhara difference; 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; 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; Adomian decomposition method; system of Whitham-Broer-Kaup equations; 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
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.