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New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus
Abstract
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- 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
- Caputo-Fabrizio derivative
- Yang transform
- Ď‘-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
- bic Book Industry Communication::G Reference, information & interdisciplinary subjects::GP Research & information: general
- bic Book Industry Communication::P Mathematics & science
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Last time updated on 11/10/2022
This paper was published in Directory of Open Access Books (DOAB).
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