Advances in Fractional Differential Operators and Their Applications

The application of generalized and fractional derivatives, such as Caputo and Riemann–Liouville derivatives, has witnessed a dramatic increase in recent years. This reprint focuses on related theoretical and applied research in areas such as the stability of time series, Lotka–Volterra systems, dist...

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Published: MDPI - Multidisciplinary Digital Publishing Institute 2023
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description The application of generalized and fractional derivatives, such as Caputo and Riemann–Liouville derivatives, has witnessed a dramatic increase in recent years. This reprint focuses on related theoretical and applied research in areas such as the stability of time series, Lotka–Volterra systems, distributed delays, Fornberg–Whitham equations, abstract evolution and fractional wave equations, cantilever beams, and fractional Riccati and Volterra equations, as well as fractional visco-elasto-plasticity, spectral theory for fractional Sturm–Liouville problems, generalized differential equations, Mittag–Leffler functions, and fractional Laplacians.
format Online
id doab-20.500.12854ir-128563
institution Directory of Open Access Books
language eng
publishDate 2023
publishDateRange 2023
publishDateSort 2023
publisher MDPI - Multidisciplinary Digital Publishing Institute
publisherStr MDPI - Multidisciplinary Digital Publishing Institute
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spelling doab-20.500.12854ir-1285632024-03-28T03:32:22Z Advances in Fractional Differential Operators and Their Applications Mingarelli, Angelo B. Zivlaei, Leila Gholizadeh Dehghan, Mohammad Mellin-Barnes integrals Sinc methods Sinc quadrature Fox functions Aleph functions Saxena function definite integrals fractional calculus fractional Langevin equation ML-kernel existence of solutions UH-type stability numerical simulation Caputo sense space-fractional Fisher’s equation cubic polynomial spline von Neumann stability fractional differential equations κ(x)-Laplacian χ-Hilfer fractional derivative existence multiplicity of solutions genus theory Concentration-Compactness Principle Mountain Pass Theorem variable exponents variational methods Fractional Sturm–Liouville Laplace transform Mittag-Leffler function eigenvalues asymptotics Cahn–Hilliard equation fractional Laplacian memory two dimensional Volterra integral equation operational matrix block pulse Taylor polynomials gradient nonlinearity fractional diffusion equation hyper-Bessel fractional partial differential equations fractional differential equation p-derivative power-law visco-elasto-plasticity time-fractional integration fractional quasi-linear viscoelasticity fractional Riccati differential equation approximate solution residual power series fractional wave equation Riemann–Liouville derivatives inverse problem determination of the order of derivative Fourier method evolution equations operator function Abel–Lidskii basis property Schatten–von Neumann class multi-order fractional differential equation stability instability Caputo derivative cantilever beam existence and uniqueness of minimizers fractional boundary value problem Euler–Lagrange theorem homotopy perturbation method fractional Fornberg–Whitham equation partial differential equation Caputo’s derivatives variational iteration method Adomian decomposition method homotopy analysis method fractional-order nonlinear system Razumikhin approach input delay distributed delay leader–following consensus Lotka–Volterra system boundedness fractional piecewise order derivative variable kernel existence of solution stability results time series sequence operator fractional-order operator model stability model perturbation analysis thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science The application of generalized and fractional derivatives, such as Caputo and Riemann–Liouville derivatives, has witnessed a dramatic increase in recent years. This reprint focuses on related theoretical and applied research in areas such as the stability of time series, Lotka–Volterra systems, distributed delays, Fornberg–Whitham equations, abstract evolution and fractional wave equations, cantilever beams, and fractional Riccati and Volterra equations, as well as fractional visco-elasto-plasticity, spectral theory for fractional Sturm–Liouville problems, generalized differential equations, Mittag–Leffler functions, and fractional Laplacians. 2023-11-30T20:31:58Z 2023-11-30T20:31:58Z 2023 book ONIX_20231130_9783036589046_15 9783036589046 9783036589053 https://directory.doabooks.org/handle/20.500.12854/128563 eng application/octet-stream Attribution 4.0 International https://mdpi.com/books/pdfview/book/8012 https://mdpi.com/books/pdfview/book/8012 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-0365-8905-3 10.3390/books978-3-0365-8905-3 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783036589046 9783036589053 374 Basel open access
spellingShingle Mellin-Barnes integrals
Sinc methods
Sinc quadrature
Fox functions
Aleph functions
Saxena function
definite integrals
fractional calculus
fractional Langevin equation
ML-kernel
existence of solutions
UH-type stability
numerical simulation
Caputo sense
space-fractional Fisher’s equation
cubic polynomial spline
von Neumann stability
fractional differential equations
κ(x)-Laplacian
χ-Hilfer fractional derivative
existence
multiplicity of solutions
genus theory
Concentration-Compactness Principle
Mountain Pass Theorem
variable exponents
variational methods
Fractional Sturm–Liouville
Laplace transform
Mittag-Leffler function
eigenvalues
asymptotics
Cahn–Hilliard equation
fractional Laplacian
memory
two dimensional Volterra integral equation
operational matrix
block pulse
Taylor polynomials
gradient nonlinearity
fractional diffusion equation
hyper-Bessel
fractional partial differential equations
fractional differential equation
p-derivative
power-law visco-elasto-plasticity
time-fractional integration
fractional quasi-linear viscoelasticity
fractional Riccati differential equation
approximate solution
residual power series
fractional wave equation
Riemann–Liouville derivatives
inverse problem
determination of the order of derivative
Fourier method
evolution equations
operator function
Abel–Lidskii basis property
Schatten–von Neumann class
multi-order fractional differential equation
stability
instability
Caputo derivative
cantilever beam
existence and uniqueness of minimizers
fractional boundary value problem
Euler–Lagrange theorem
homotopy perturbation method
fractional Fornberg–Whitham equation
partial differential equation
Caputo’s derivatives
variational iteration method
Adomian decomposition method
homotopy analysis method
fractional-order nonlinear system
Razumikhin approach
input delay
distributed delay
leader–following consensus
Lotka–Volterra system
boundedness
fractional piecewise order derivative
variable kernel
existence of solution
stability results
time series
sequence operator
fractional-order operator
model stability
model perturbation analysis
thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general
thema EDItEUR::P Mathematics and Science
Advances in Fractional Differential Operators and Their Applications
title Advances in Fractional Differential Operators and Their Applications
title_full Advances in Fractional Differential Operators and Their Applications
title_fullStr Advances in Fractional Differential Operators and Their Applications
title_full_unstemmed Advances in Fractional Differential Operators and Their Applications
title_short Advances in Fractional Differential Operators and Their Applications
title_sort advances in fractional differential operators and their applications
topic Mellin-Barnes integrals
Sinc methods
Sinc quadrature
Fox functions
Aleph functions
Saxena function
definite integrals
fractional calculus
fractional Langevin equation
ML-kernel
existence of solutions
UH-type stability
numerical simulation
Caputo sense
space-fractional Fisher’s equation
cubic polynomial spline
von Neumann stability
fractional differential equations
κ(x)-Laplacian
χ-Hilfer fractional derivative
existence
multiplicity of solutions
genus theory
Concentration-Compactness Principle
Mountain Pass Theorem
variable exponents
variational methods
Fractional Sturm–Liouville
Laplace transform
Mittag-Leffler function
eigenvalues
asymptotics
Cahn–Hilliard equation
fractional Laplacian
memory
two dimensional Volterra integral equation
operational matrix
block pulse
Taylor polynomials
gradient nonlinearity
fractional diffusion equation
hyper-Bessel
fractional partial differential equations
fractional differential equation
p-derivative
power-law visco-elasto-plasticity
time-fractional integration
fractional quasi-linear viscoelasticity
fractional Riccati differential equation
approximate solution
residual power series
fractional wave equation
Riemann–Liouville derivatives
inverse problem
determination of the order of derivative
Fourier method
evolution equations
operator function
Abel–Lidskii basis property
Schatten–von Neumann class
multi-order fractional differential equation
stability
instability
Caputo derivative
cantilever beam
existence and uniqueness of minimizers
fractional boundary value problem
Euler–Lagrange theorem
homotopy perturbation method
fractional Fornberg–Whitham equation
partial differential equation
Caputo’s derivatives
variational iteration method
Adomian decomposition method
homotopy analysis method
fractional-order nonlinear system
Razumikhin approach
input delay
distributed delay
leader–following consensus
Lotka–Volterra system
boundedness
fractional piecewise order derivative
variable kernel
existence of solution
stability results
time series
sequence operator
fractional-order operator
model stability
model perturbation analysis
thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general
thema EDItEUR::P Mathematics and Science
topic_facet Mellin-Barnes integrals
Sinc methods
Sinc quadrature
Fox functions
Aleph functions
Saxena function
definite integrals
fractional calculus
fractional Langevin equation
ML-kernel
existence of solutions
UH-type stability
numerical simulation
Caputo sense
space-fractional Fisher’s equation
cubic polynomial spline
von Neumann stability
fractional differential equations
κ(x)-Laplacian
χ-Hilfer fractional derivative
existence
multiplicity of solutions
genus theory
Concentration-Compactness Principle
Mountain Pass Theorem
variable exponents
variational methods
Fractional Sturm–Liouville
Laplace transform
Mittag-Leffler function
eigenvalues
asymptotics
Cahn–Hilliard equation
fractional Laplacian
memory
two dimensional Volterra integral equation
operational matrix
block pulse
Taylor polynomials
gradient nonlinearity
fractional diffusion equation
hyper-Bessel
fractional partial differential equations
fractional differential equation
p-derivative
power-law visco-elasto-plasticity
time-fractional integration
fractional quasi-linear viscoelasticity
fractional Riccati differential equation
approximate solution
residual power series
fractional wave equation
Riemann–Liouville derivatives
inverse problem
determination of the order of derivative
Fourier method
evolution equations
operator function
Abel–Lidskii basis property
Schatten–von Neumann class
multi-order fractional differential equation
stability
instability
Caputo derivative
cantilever beam
existence and uniqueness of minimizers
fractional boundary value problem
Euler–Lagrange theorem
homotopy perturbation method
fractional Fornberg–Whitham equation
partial differential equation
Caputo’s derivatives
variational iteration method
Adomian decomposition method
homotopy analysis method
fractional-order nonlinear system
Razumikhin approach
input delay
distributed delay
leader–following consensus
Lotka–Volterra system
boundedness
fractional piecewise order derivative
variable kernel
existence of solution
stability results
time series
sequence operator
fractional-order operator
model stability
model perturbation analysis
thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general
thema EDItEUR::P Mathematics and Science
url ONIX_20231130_9783036589046_15