Fractional-Order Integral and Derivative Operators and Their Applications

[...]encouraged by the noteworthy successes of this series of four Special Issues, as well as of (for example) two other Special Issues of Axioms, on the subject-areas of “Mathematical Analysis and Applications” and “Mathematical Analysis and Applications II”, Axioms has already started the publicat...

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Published in:Mathematics (Basel) Vol. 8; no. 6; p. 1016
Main Author: Srivastava, Hari Mohan
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.06.2020
Subjects:
Applications of mathematics
Applied mathematics
Axioms
Banach spaces
Boundary conditions
Boundary value problems
Calculus
Collection
Controllability
Correlation coefficients
Derivatives
Editorials
Fractional calculus
Fuzzy systems
Hermite polynomials
HIV
Human immunodeficiency virus
Hypergeometric functions
Identities
Integrals
Landsat satellites
Matrix methods
n/a
Operators (mathematics)
Pantographs
Partial differential equations
Potassium
Prophylaxis
Satellite imagery
Theory
Variables
Switzerland
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:[...]encouraged by the noteworthy successes of this series of four Special Issues, as well as of (for example) two other Special Issues of Axioms, on the subject-areas of “Mathematical Analysis and Applications” and “Mathematical Analysis and Applications II”, Axioms has already started the publication of a Topical Collection, entitled “Mathematical Analysis and Applications” (Collection Editor: H. M. Srivastava), with an open submission deadline. Operators of fractional calculus and their applications; Chaos and fractional dynamics; Fractional-order ODEs and PDEs; Fractional-order differintegral equations; Fractional-order integro-differential equations; Fractional-order integrals and fractional-order derivatives associated with special functions of mathematical physics and applied mathematics; Identities and inequalities involving fractional-order integrals and fractional-order derivatives; Dynamical systems based upon fractional calculus. Some of the notable contributions in this volume happen to have successfully addressed such topics of fractional calculus and related mathematical analysis as (for example) operational matrix of fractional-order derivatives for solving systems of fractional differential equations via Legendre wavelets, Hermite polynomial approach for solving the SIR model of epidemics, the extremal solution to conformable fractional differential equations involving integral boundary condition, approximate controllability of sub-diffusion equation with impulsive condition, incomplete hypergeometric functions and incomplete Riemann-Liouville fractional integral operators, random coupled Hilfer and Hadamard fractional differential systems in generalized Banach spaces, uniqueness and existence of approximate solution to initial value problem for fractional differential equation of variable order involving the derivative arguments on the half-axis, solvability of a mixed problem for a high-order partial differential equation with fractional derivatives with respect to time, with Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes, fractional-calculus connections between Mittag–Leffler functions, impact of fractional calculus on correlation coefficient between available potassium and spectrum data in ground hyperspectral and Landsat 8 image, efficacy of the post-exposure prophylaxis and of the HIV latent reservoir in HIV infection, fractional-order unknown inputs fuzzy observer for Takagi–Sugeno systems with unmeasurable premise variables, stability results for implicit fractional pantograph differential equations viaφ -Hilfer fractional derivative with a nonlocal Riemann-Liouville fractional integral condition, and so on. In connection with such works as (for example) [4,18], and indeed also many papers included in the published volumes [23,24,25,26], a recent survey-cum-expository review article [27] will be potentially useful in order to motivate further researches and developments involving a wide variety of operators of basic (or q-) calculus and fractional q-calculus and their widespread applications in Geometric Function Theory of Complex Analysis.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math8061016