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Applied Mathematics and Fractional Calculus
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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.
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Keywords
- Aboodh transform iterative method
- Adomian decomposition method
- anisotropic Lorentz space
- approximate endpoint criterion
- approximate solutions
- Atangana–Baleanu fractional derivative
- Babenko’s approach
- Banach fixed point theorem
- Bessel polynomials
- bilateral tempered fractional derivative
- boundary value problem
- Caputo derivative
- Caputo fractional derivative
- Caputo Operator
- Caputo q-derivative
- Caputo–Fabrizio and Atangana-Baleanu operators
- collocation method
- collocation points
- concave operator
- condensing function
- conservation laws
- convergence analysis
- Convex functions
- degenerate evolution equation
- discrete fractional calculus
- eigenfunctions and eigenvalues
- elastic beam problem
- equations
- Euler–Lagrange equation
- existence
- existence and uniqueness
- existence of solutions
- first fundamental theorem of fractional calculus
- fixed point
- fixed point theorem
- fractional burgers equation
- Fractional calculus
- fractional derivative
- fractional derivatives
- fractional differential equation
- fractional differential equations
- fractional Dzhrbashyan–Nersesyan derivative
- fractional Fornberg–Whitham equation (FWE)
- fractional Kadomtsev-Petviashvili system
- fractional KdV equation
- fractional Prabhakar derivatives
- fractional Sturm–Liouville problems
- Fredholm–Volterra integral Equations
- gamma function
- Gelfand problem
- general fractional derivative of arbitrary order
- general fractional integral of arbitrary order
- Green’s function
- hermite cubic spline
- HHF type inequality
- initial boundary value problem
- initial value problem
- integral transform
- lie group analysis
- Mathematics & science
- MHD equations
- Mittag–Leffler function
- nabla fractional difference
- natural boundary conditions
- natural transform
- new iterative transform method
- nonlocal conditions
- one-sided tempered fractional derivative
- optimal controls
- order cone
- partial differential equation
- partial Riemann–Liouville fractional integral
- power series solutions
- quantum integro-difference BVP
- Reference, information & interdisciplinary subjects
- regularity criteria
- Research & information: general
- Riemann–Liouville derivative
- Riemann–Liouville fractional difference operator
- Riemann–Liouville q-integral
- second fundamental theorem of fractional calculus
- semigroup theory
- separated boundary conditions
- Shehu decomposition method
- Shehu transform
- singular sum fractional q-differential
- Sonine kernel
- Symmetry
- tempered fractional derivative
- tempered riesz potential
- time delay
- time-fractional Kaup–Kupershmidt equation
- Ulam stability
- weak solution
- weighted fractional operators
- ρ-Laplace decomposition method
- ρ-Laplace variational iteration method
- φ-Hilfer fractional system with impulses
Links
DOI: 10.3390/books978-3-0365-5147-0Editions