Choose an application

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

This volume consists of a collection of 14 accepted submissions (including several invited feature articles) to the Special Issue of MDPI's journal Symmetry on the general subject area of integral transformations, operational calculus and their applications from many different parts around the world. The main objective of the Special Issue was to gather review, expository, and original research articles dealing with the state-of-the-art advances in integral transformations and operational calculus as well as their multidisciplinary applications, together with some relevance to the aspect of symmetry. Various families of fractional-order integrals and derivatives have been found to be remarkably important and fruitful, mainly due to their demonstrated applications in numerous diverse and widespread areas of mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional-order operators provide potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables.

History of engineering & technology --- Stancu-type Bernstein operators --- Bézier bases --- Voronovskaja-type theorems --- modulus of continuity --- rate of convergence --- bivariate operators --- approximation properties --- statistical convergence --- P-convergent --- statistically and relatively modular deferred-weighted summability --- relatively modular deferred-weighted statistical convergence --- Korovkin-type approximation theorem --- modular space --- convex space --- N-quasi convex modular --- N-quasi semi-convex modular --- vehicle collaborative content downloading --- fuzzy comprehensive evaluation --- VANET --- delay differential equations --- integral operator --- periodic solutions --- subordinations --- exponential function --- Hankel determinant --- fractional differential equations with input --- Mittag-Leffler stability --- left generalized fractional derivative --- ρ-Laplace transforms --- functional integral equations --- Banach algebra --- fixed point theorem --- measure of noncompactness --- Geometric Function Theory --- q-integral operator --- q-starlike functions of complex order --- q-convex functions of complex order --- (δ,q)-neighborhood --- meromorphic multivalent starlike functions --- subordination --- univalent function --- symmetric differential operator --- unit disk --- analytic function --- analytic functions --- conic region --- Hadamard product --- differential subordination --- differential superordination --- generalized fractional differintegral operator --- Convex function --- Simpson’s rule --- differentiable function --- weights --- positive integral operators --- convolution operators --- n/a --- Bézier bases --- Simpson's rule

Choose an application

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

This volume consists of a collection of 14 accepted submissions (including several invited feature articles) to the Special Issue of MDPI's journal Symmetry on the general subject area of integral transformations, operational calculus and their applications from many different parts around the world. The main objective of the Special Issue was to gather review, expository, and original research articles dealing with the state-of-the-art advances in integral transformations and operational calculus as well as their multidisciplinary applications, together with some relevance to the aspect of symmetry. Various families of fractional-order integrals and derivatives have been found to be remarkably important and fruitful, mainly due to their demonstrated applications in numerous diverse and widespread areas of mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional-order operators provide potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables.

Stancu-type Bernstein operators --- Bézier bases --- Voronovskaja-type theorems --- modulus of continuity --- rate of convergence --- bivariate operators --- approximation properties --- statistical convergence --- P-convergent --- statistically and relatively modular deferred-weighted summability --- relatively modular deferred-weighted statistical convergence --- Korovkin-type approximation theorem --- modular space --- convex space --- N-quasi convex modular --- N-quasi semi-convex modular --- vehicle collaborative content downloading --- fuzzy comprehensive evaluation --- VANET --- delay differential equations --- integral operator --- periodic solutions --- subordinations --- exponential function --- Hankel determinant --- fractional differential equations with input --- Mittag-Leffler stability --- left generalized fractional derivative --- ρ-Laplace transforms --- functional integral equations --- Banach algebra --- fixed point theorem --- measure of noncompactness --- Geometric Function Theory --- q-integral operator --- q-starlike functions of complex order --- q-convex functions of complex order --- (δ,q)-neighborhood --- meromorphic multivalent starlike functions --- subordination --- univalent function --- symmetric differential operator --- unit disk --- analytic function --- analytic functions --- conic region --- Hadamard product --- differential subordination --- differential superordination --- generalized fractional differintegral operator --- Convex function --- Simpson’s rule --- differentiable function --- weights --- positive integral operators --- convolution operators --- n/a --- Bézier bases --- Simpson's rule

Choose an application

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

This volume is a collection of investigations involving the theory and applications of the various tools and techniques of mathematical analysis and analytic number theory, which are remarkably widespread in many diverse areas of the mathematical, biological, physical, chemical, engineering, and statistical sciences. It contains invited and welcome original as well as review-cum-expository research articles dealing with recent and new developments on the topics of mathematical analysis and analytic number theory as well as their multidisciplinary applications.

subordination --- functions with positive real part --- reciprocals --- univalent functions --- starlikeness --- convexity --- close-to-convexity --- hyper-Bessel functions --- Hardy space --- distribution --- fractional Laplacian --- Riesz fractional derivative --- delta sequence --- convolution --- subordinations --- starlike functions --- convex functions --- close-to-convex functions --- cardioid domain --- Hankel determinant --- m-fold symmetric functions --- harmonic univalent functions --- with symmetric conjecture point --- integral expressions --- coefficient estimates --- distortion --- umbral methods --- harmonic numbers --- special functions --- integral representations --- laplace and other integral transforms --- analytic functions --- quasi-Hadamard --- differential operator --- closure property --- riemann zeta function --- asymptotics --- exponential sums --- multivalent functions --- q-Ruschweyh differential operator --- q-starlike functions --- circular domain --- q-Bernardi integral operator --- Bessel functions --- Appell–Bessel functions --- generating functions --- Chebyshev polynomials --- Euler sums --- Catalan’s constant --- Trigamma function --- integral representation --- closed form --- ArcTan and ArcTanh functions --- partial fractions --- Lambert series --- cotangent sum --- modular transformation --- Dedekind sum --- lemniscate of Bernoulli Hankel determinant --- determinant --- inverse --- Mersenne number --- periodic tridiagonal Toeplitz matrix --- Sherman-Morrison-Woodbury formula --- Fibonacci number --- Lucas number --- Toeplitz matrix --- Hankel matrix --- univalent function --- second Hankel determinant --- bi-close-to-convex functions --- gamma function and its extension --- Pochhammer symbol and its extensions --- hypergeometric function and its extensions --- τ-Gauss hypergeometric function and its extensions --- τ-Kummer hypergeometric function --- Fox-Wright function --- p-valent analytic function --- Hadamard product --- q-integral operator --- generalized Lupaş operators --- q analogue --- Korovkin’s type theorem --- convergence theorems --- Voronovskaya type theorem --- starlike function --- subordinate --- Janowski functions --- conic domain --- q-convex functions --- q-close-to-convex functions --- theta-function identities --- multivariable R-functions --- Jacobi’s triple-product identity --- Ramanujan’s theta functions --- q-product identities --- Euler’s pentagonal number theorem --- Rogers-Ramanujan continued fraction --- Rogers-Ramanujan identities --- combinatorial partition-theoretic identities --- Schur’s, the Göllnitz-Gordon’s and the Göllnitz’s partition identities --- Schur’s second partition theorem