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New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus
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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
- AB-fractional operator
- Adomian decomposition method
- asymptotic stability
- Atangana–Baleanu fractional derivative operator
- basin of attraction
- Bessel function
- beta function
- boundedness
- Caputo derivative
- Caputo fractional derivative
- Caputo-Fabrizio derivative
- Caputo–Fabrizio derivative
- Caputo–Hadamard fractional derivative
- Caputo–Hadamard fractional integral
- Cattaneo equation
- computational cost
- computational order of convergence
- convex
- cubic B-splines
- delta function
- efficiency index
- Elzaki transform
- Euler’s integral of gamma functions
- exponential convex
- extended cubic B-splines
- extremal solutions
- Fejér–Hadamard inequality
- Fisher’s equation
- fixed point theory
- Fornberg–Whitham equation
- Fox–Wright-function
- fractal dimensions
- fractional
- Fractional calculus
- fractional div-curl systems
- fractional kinetic equation
- fractional transforms
- fractional vector operators
- fractional-order differential equations
- generalized fractional kinetic equation
- generalized hypergeometric series
- Gould-Hopper-Laguerre-Sheffer matrix polynomials
- Hadamard inequality
- Halley’s method
- harmonically convex function
- Helmholtz decomposition theorem
- Hermite-Hadamard-type inequalities
- Hilfer fractional derivative
- Hölder’s inequality
- Hukuhara difference
- hybrid Caputo–Hadamard fractional differential equation and inclusion
- hybrid control
- inequalities
- Mathematics & science
- Mittag–Leffler kernel
- model calibration
- monotone iterative method
- n/a
- Neimark-Sacker bifurcation
- new iterative transform method
- non-singular function involving kernel fractional operator
- nonlinear models
- operational matrices
- operational methods
- period-doubling bifurcation
- prey-predator model
- quantum
- quasi-monomiality
- Reference, information & interdisciplinary subjects
- Research & information: general
- Riemann zeta-function
- Riemann–Liouville derivative
- Sequences
- shifted Vieta–Lucas polynomials
- system of Whitham-Broer-Kaup equations
- thermostat modeling
- trigonometric cubic B-splines
- typhoid fever disease
- umbral calculus
- vaccination
- weighted (k,s) fractional derivative
- weighted (k,s) fractional integral operator
- weighted generalized Laplace transform
- Yang transform
- ϑ-Caputo derivative
Links
DOI: 10.3390/books978-3-0365-4906-4Editions