Applied Mathematics and Fractional Calculus II

• Format: eBook
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: Appell polynomials; averaging principle; Bessel functions; BHCS algorithm; Boehmian; boundary conditions; boundary value problems; Caputo fractional derivatives; compact support; composition operators; controllability; convolution; cosine and sine family; coupled system; Cuckoo search; delays; delta sequences; Dunkl theory; equivalence class; Erdélyi-type integral; exact solution; existence; existence and uniqueness; finite delay; fixed point; fixed point theorems; fixed-point theory; fractional calculus; fractional derivative; fractional derivatives; fractional differential equation; fractional differential equations (FDEs); fractional Hilbert transform; fractional Integral; fractional integral operator; fractional integro-differential equations; fractional Klein–Gordon equation; fractional optimal control problems (FOCPs); free terminal time; functional differential equation; generalized fourth order Runge–Kutta method; generalized fractional derivatives; generalized fractional integrals; generalized hypergeometric function; generalized proportional fractional derivatives; global existence; heat conduction; Hermite polynomials; Hilbert transform; homotopy perturbation method; human head; instantaneous impulses; integral inequalities; integral transforms; Janssen vaccine; Lp convergence; Lyapunov functions; Mathematics and Science; midpoint formula; mild solution; mild solutions; Mittag–Leffler stability; Moderna vaccine; Mohand transform; Navier–Stokes equations; non-instantaneous impulses; numerical method; operational rule; optimal control; Pfizer vaccine; Poisson jumps; random fixed point; Razumikhin method; Reference, Information and Interdisciplinary subjects; regularity; Research and information: general; Riemann–Liouville fractional derivative; s-convex functions; series solution; shock wave equation; sinusoidal; state dependent delay; theta finite difference method; three-variable Hermite-based Appell polynomials; variable-order hybrid operator; weakly coupled system of equations; weighted integral; Yang transform; θ-evolution equation; ψ-Capuo fractional stochastic delay differential equations
• ISBN: 9783036594255; 3036594248; 3036594256; 9783036594248
• DOI: 10.3390/books978-3-0365-9424-8

In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to studying integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until a few 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, and entropy theory. Since fractional order's differential and integral operators 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 applying fractional calculus theory has become a focus of international academic research. This Special Issue, “Applied Mathematics and Fractional Calculus II,” 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 the USA, Ireland, Romania, Bulgaria, Türkiye, China, Pakistan, Iran, Egypt, India, Iraq, and Saudi Arabia.