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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

generalized Laguerre --- central complete Bell numbers --- rational polynomials --- Changhee polynomials of type two --- Euler polynomials --- generalized Laguerre polynomials --- Hermite --- conjecture --- Legendre --- the degenerate gamma function --- trivariate Lucas polynomials --- perfectly matched layer --- third-order character --- Euler numbers --- two variable q-Berstein operator --- entropy production --- hypergeometric function --- q-Bernoulli numbers --- q-Bernoulli polynomials --- symmetry group --- Bernoulli polynomials --- Fibonacci polynomials --- central incomplete Bell polynomials --- Chebyshev polynomials --- convolution sums --- Lucas polynomials --- Jacobi --- the modified degenerate Laplace transform --- q-Volkenborn integral on ?p --- and fourth kinds --- two variable q-Berstein polynomial --- the modified degenerate gamma function --- two variable q-Bernstein operators --- reduction method --- identity --- elementary and combinatorial methods --- generalized Bernoulli polynomials and numbers attached to a Dirichlet character ? --- explicit relations --- recursive sequence --- Fubini polynomials --- p-adic integral on ?p --- generating functions --- q-Euler number --- acoustic wave equation --- congruence --- trivariate Fibonacci polynomials --- stochastic thermodynamics --- fermionic p-adic integrals --- Laguerre polynomials --- fluctuation theorem --- Bernoulli numbers and polynomials --- w-torsion Fubini polynomials --- non-equilibrium free energy --- hypergeometric functions 1F1 and 2F1 --- recursive formula --- Chebyshev polynomials of the first --- second --- central complete Bell polynomials --- Apostol-type Frobenius–Euler polynomials --- sums of finite products --- q-Euler polynomial --- symmetric identities --- stability --- fermionic p-adic q-integral on ?p --- Gegenbauer polynomials --- continued fraction --- thermodynamics of information --- well-posedness --- fermionic p-adic integral on ?p --- catalan numbers --- classical Gauss sums --- three-variable Hermite polynomials --- q-Changhee polynomials --- Catalan numbers --- two variable q-Bernstein polynomials --- q-Euler polynomials --- analytic method --- representation --- mutual information --- Fibonacci --- Legendre polynomials --- Gegenbauer --- generalized Bernoulli polynomials and numbers of arbitrary complex order --- Lucas --- elementary method --- new sequence --- third --- the degenerate Laplace transform --- computational formula --- operational connection --- sums of finite products of Chebyshev polynomials of the third and fourth kinds --- Changhee polynomials --- linear form in logarithms

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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.

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 --- 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 --- Fejér-Hadamard inequality --- Fisher's equation --- Atangana-Baleanu fractional derivative operator --- Mittag-Leffler kernel --- Fornberg-Whitham equation --- Riemann-Liouville derivative --- Halley's method --- Caputo-Hadamard fractional derivative --- Caputo-Hadamard fractional integral --- hybrid Caputo-Hadamard fractional differential equation and inclusion --- Hölder's inequality --- shifted Vieta-Lucas polynomials --- Euler's integral of gamma functions --- Fox-Wright-function

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

Research & information: general --- Mathematics & science --- OWA operator --- RIM quantifier --- maximum entropy --- minimax ratio --- generating function --- minimal variability --- minimax disparity --- solution equivalence --- fuzzy sets --- extended minimax disparity --- OWA model --- RIM quantifier problem --- extended degenerate r-central factorial numbers of the second kind --- extended degenerate r-central bell polynomials --- type 2 Bernoulli polynomials --- type 2 Euler polynomials --- identities of symmetry --- Laplace distribution --- Fibonacci polynomials --- Lucas polynomials --- sums of powers --- divisible properties --- R. S. Melham’s conjectures --- degenerate Bernoulli polynomials --- degenerate Bernstein operators --- extended r-central complete bell polynomials --- extended r-central incomplete bell polynomials --- complete r-Bell polynomials --- incomplete r-bell polynomials --- Fibonacci numbers --- Lucas numbers --- Chebyshev polynomials --- Legendre polynomials --- Jacobi polynomials --- Gegenbauer polynomials --- convolution formula --- Bernoulli polynomials --- random variables --- p-adic invariant integral on Zp --- integer power sums polynomials --- Stirling polynomials of the second kind --- degenerate Stirling polynomials of the second kind --- type 2 degenerate q-Bernoulli polynomials --- p-adic q-integral --- balancing numbers --- balancing polynomials --- combinatorial methods --- symmetry sums --- Chebyshev polynomials of the first kind --- power series --- polynomial identities --- polynomial inequalities --- Waring–Goldbach problem --- circle method --- exceptional set --- symmetric form --- type 2 degenerate Bernoulli polynomials of the second kind --- degenerate central factorial numbers of the second kind --- degenerate poly-Bernoulli polynomials --- degenerate poly-Genocchi polynomials --- stirling numbers --- Erdős-Ko-Rado theorem --- intersecting families --- polynomial method --- n/a --- polylogarithm functions --- poly-Genocchi polynomials --- unipoly functions --- unipoly Genocchi polynomials --- R. S. Melham's conjectures --- Waring-Goldbach problem --- Erdős-Ko-Rado theorem

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

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 --- 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 --- 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 --- 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