TY - BOOK ID - 145974104 TI - Applied Mathematics and Fractional Calculus AU - González, Francisco Martínez AU - Kaabar, Mohammed K. A. PY - 2022 PB - Basel MDPI Books DB - UniCat KW - Research & information: general KW - Mathematics & science KW - condensing function KW - approximate endpoint criterion KW - quantum integro-difference BVP KW - existence KW - fractional Kadomtsev-Petviashvili system KW - lie group analysis KW - power series solutions KW - convergence analysis KW - conservation laws KW - symmetry KW - weighted fractional operators KW - convex functions KW - HHF type inequality KW - fractional calculus KW - Euler–Lagrange equation KW - natural boundary conditions KW - time delay KW - MHD equations KW - weak solution KW - regularity criteria KW - anisotropic Lorentz space KW - Sonine kernel KW - general fractional derivative of arbitrary order KW - general fractional integral of arbitrary order KW - first fundamental theorem of fractional calculus KW - second fundamental theorem of fractional calculus KW - ρ-Laplace variational iteration method KW - ρ-Laplace decomposition method KW - partial differential equation KW - caputo operator KW - fractional Fornberg–Whitham equation (FWE) KW - Riemann–Liouville fractional difference operator KW - boundary value problem KW - discrete fractional calculus KW - existence and uniqueness KW - Ulam stability KW - elastic beam problem KW - tempered fractional derivative KW - one-sided tempered fractional derivative KW - bilateral tempered fractional derivative KW - tempered riesz potential KW - collocation method KW - hermite cubic spline KW - fractional burgers equation KW - fractional differential equation KW - fractional Dzhrbashyan–Nersesyan derivative KW - degenerate evolution equation KW - initial value problem KW - initial boundary value problem KW - partial Riemann–Liouville fractional integral KW - Babenko’s approach KW - Banach fixed point theorem KW - Mittag–Leffler function KW - gamma function KW - nabla fractional difference KW - separated boundary conditions KW - Green’s function KW - existence of solutions KW - Caputo q-derivative KW - singular sum fractional q-differential KW - fixed point KW - equations KW - Riemann–Liouville q-integral KW - Shehu transform KW - Caputo fractional derivative KW - Shehu decomposition method KW - new iterative transform method KW - fractional KdV equation KW - approximate solutions KW - Riemann–Liouville derivative KW - concave operator KW - fixed point theorem KW - Gelfand problem KW - order cone KW - integral transform KW - Atangana–Baleanu fractional derivative KW - Aboodh transform iterative method KW - φ-Hilfer fractional system with impulses KW - semigroup theory KW - nonlocal conditions KW - optimal controls KW - fractional derivatives KW - fractional Prabhakar derivatives KW - fractional differential equations KW - fractional Sturm–Liouville problems KW - eigenfunctions and eigenvalues KW - Fredholm–Volterra integral Equations KW - fractional derivative KW - Bessel polynomials KW - Caputo derivative KW - collocation points KW - Caputo–Fabrizio and Atangana-Baleanu operators KW - time-fractional Kaup–Kupershmidt equation KW - natural transform KW - Adomian decomposition method KW - condensing function KW - approximate endpoint criterion KW - quantum integro-difference BVP KW - existence KW - fractional Kadomtsev-Petviashvili system KW - lie group analysis KW - power series solutions KW - convergence analysis KW - conservation laws KW - symmetry KW - weighted fractional operators KW - convex functions KW - HHF type inequality KW - fractional calculus KW - Euler–Lagrange equation KW - natural boundary conditions KW - time delay KW - MHD equations KW - weak solution KW - regularity criteria KW - anisotropic Lorentz space KW - Sonine kernel KW - general fractional derivative of arbitrary order KW - general fractional integral of arbitrary order KW - first fundamental theorem of fractional calculus KW - second fundamental theorem of fractional calculus KW - ρ-Laplace variational iteration method KW - ρ-Laplace decomposition method KW - partial differential equation KW - caputo operator KW - fractional Fornberg–Whitham equation (FWE) KW - Riemann–Liouville fractional difference operator KW - boundary value problem KW - discrete fractional calculus KW - existence and uniqueness KW - Ulam stability KW - elastic beam problem KW - tempered fractional derivative KW - one-sided tempered fractional derivative KW - bilateral tempered fractional derivative KW - tempered riesz potential KW - collocation method KW - hermite cubic spline KW - fractional burgers equation KW - fractional differential equation KW - fractional Dzhrbashyan–Nersesyan derivative KW - degenerate evolution equation KW - initial value problem KW - initial boundary value problem KW - partial Riemann–Liouville fractional integral KW - Babenko’s approach KW - Banach fixed point theorem KW - Mittag–Leffler function KW - gamma function KW - nabla fractional difference KW - separated boundary conditions KW - Green’s function KW - existence of solutions KW - Caputo q-derivative KW - singular sum fractional q-differential KW - fixed point KW - equations KW - Riemann–Liouville q-integral KW - Shehu transform KW - Caputo fractional derivative KW - Shehu decomposition method KW - new iterative transform method KW - fractional KdV equation KW - approximate solutions KW - Riemann–Liouville derivative KW - concave operator KW - fixed point theorem KW - Gelfand problem KW - order cone KW - integral transform KW - Atangana–Baleanu fractional derivative KW - Aboodh transform iterative method KW - φ-Hilfer fractional system with impulses KW - semigroup theory KW - nonlocal conditions KW - optimal controls KW - fractional derivatives KW - fractional Prabhakar derivatives KW - fractional differential equations KW - fractional Sturm–Liouville problems KW - eigenfunctions and eigenvalues KW - Fredholm–Volterra integral Equations KW - fractional derivative KW - Bessel polynomials KW - Caputo derivative KW - collocation points KW - Caputo–Fabrizio and Atangana-Baleanu operators KW - time-fractional Kaup–Kupershmidt equation KW - natural transform KW - Adomian decomposition method UR - https://www.unicat.be/uniCat?func=search&query=sysid:145974104 AB - In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia. ER -