Applied Mathematics and Fractional Calculus II

• Other Authors: González, Francisco Martínez (Editor), Kaabar, Mohammed K. A. (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: Research & information: general; Mathematics & science; fractional Klein-Gordon equation; Yang transform; homotopy perturbation method; series solution; Mohand transform; shock wave equation; composition operators; Erdélyi-type integral; fractional integral operator; generalized hypergeometric function; convolution; Boehmian; fractional Hilbert transform; Hilbert transform; equivalence class; delta sequences; compact support; generalized fractional derivatives; generalized fractional integrals; coupled system; existence; fixed point; generalized proportional fractional derivatives; delays; non-instantaneous impulses; instantaneous impulses; Mittag-Leffler stability; Razumikhin method; Lyapunov functions; fractional calculus; fixed-point theory; Riemann-Liouville fractional derivative; fractional differential equation; sinusoidal; exact solution; fractional integro-differential equations; boundary conditions; existence and uniqueness; fixed point theorems; random fixed point; state dependent delay; controllability; functional differential equation; mild solution; finite delay; cosine and sine family; Navier-Stokes equations; Caputo fractional derivatives; mild solutions; regularity; fractional derivatives; weighted integral; midpoint formula; integral inequalities; s-convex functions; optimal control; fractional differential equations (FDEs); fractional optimal control problems (FOCPs); free terminal time; Hermite polynomials; Appell polynomials; three-variable Hermite-based Appell polynomials; fractional derivative; integral transforms; operational rule; variable-order hybrid operator; Pfizer vaccine; Moderna vaccine; Janssen vaccine; theta finite difference method; generalized fourth order Runge-Kutta method; θ-evolution equation; weakly coupled system of equations; global existence; averaging principle; ψ-Capuo fractional stochastic delay differential equations; Poisson jumps; Lp convergence; boundary value problems; heat conduction; BHCS algorithm; Cuckoo search; numerical method; human head; Dunkl theory; fractional Integral; Bessel functions
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.