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Recent Advances in Fractional Calculus
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This project is dedicated to fractional calculus, one of the most dynamic areas of mathematical science today. For 50 years, the number of researchers and scientific publications dealing with this topic has been increasing day by day, which clearly demonstrates the growing interest in fractional calculus, both from a practical and a theoretical point of view. The purpose of this reprint is to extend existing results in fractional calculus by considering various types of fractional operators, such as Caputo-type, Hilfer-type, and Riemann–Liouville-type, by introducing various types of inequalities, such as Bullen-type, Jensen–Mercer-type, and Hermite–Hadamard-type, as well as by analyzing fractional-order differential equations and boundary value problems.
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Keywords
- (h,m)-convex functions
- Analytic functions
- boundary value problems for non-linear parabolic PDE
- Bullen’s inequality
- Caputo
- Caputo fractional derivative
- close-to-convex functions
- coincidence degree
- complex order
- convergence of numerical methods
- Convex functions
- convolution
- countability
- coupled nonlocal boundary conditions
- COVID-19
- dynamic boundary conditions
- Error analysis
- evolution equation
- existence of solutions
- Faber polynomial expansion
- fixed point theorems
- fractional derivative
- fractional derivatives
- fractional integral operators
- fractional integrals
- fractional order
- fractional step method
- fractional-order
- Hadamard inequality
- half-line
- Hermite–Hadamard inequality
- Hölder inequality
- infinite time-delay
- Jensen–Mercer inequality
- Kuratowski measure of noncompactness
- m-fold symmetric functions
- m-point
- Mathematical model
- meromorphic function
- mild solution
- n/a
- Neighborhoods
- non-conformable fractional operators
- numerical algorithm
- Optimal Control
- partial sums
- power mean
- Power mean inequality
- q-convex
- q-fractional derivative
- q-nalogue of linear differential operator
- q-starlike
- quantum (or q-) calculus
- resonance
- shedding effect
- systems of (k,?) Hilfer fractional differential equations
- thema EDItEUR::U Computing and Information Technology::UY Computer science
Links
DOI: 10.3390/books978-3-7258-1237-0Editions