Special Issue "Recent Developments in the Theory and Applications of Fractional Calculus"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (30 April 2017).

Special Issue Editor

Prof. Dr. Hari Mohan Srivastava
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Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Interests: real and complex analysis; fractional calculus and its applications; integral equations and transforms; higher transcendental functions and their applications; q-series and q-polynomials; analytic number theory; analytic and geometric Inequalities; probability and statistics; inventory modelling and optimization
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Special Issue Information

Dear Colleagues,

The subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. It does indeed provide several potentially useful tools for solving differential, integral and integro-differential equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. Both review, expository and original research articles dealing with the recent advances in the theory fractional calculus and its multidisciplinary applications are invited for this Special Issue.

Prof. Dr. Hari M. Srivastava
Guest Editor

Manuscript Submission Information

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Keywords

  • Fractional differential equations
  • Fractional Dynamics and Chaos
  • Fractional differintegral equations
  • Fractional integro-differential equations
  • Fractional integrals and fractional derivatives associated with special functions of mathematical physics
  • Inequalities and identities involving fractional integrals and fractional derivatives

Published Papers (3 papers)

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Research

Open AccessArticle
An Analysis on the Fractional Asset Flow Differential Equations
Mathematics 2017, 5(2), 33; https://doi.org/10.3390/math5020033 - 16 Jun 2017
Cited by 2
Abstract
The asset flow differential equation (AFDE) is the mathematical model that plays an essential role for planning to predict the financial behavior in the market. In this paper, we introduce the fractional asset flow differential equations (FAFDEs) based on the Liouville-Caputo derivative. We [...] Read more.
The asset flow differential equation (AFDE) is the mathematical model that plays an essential role for planning to predict the financial behavior in the market. In this paper, we introduce the fractional asset flow differential equations (FAFDEs) based on the Liouville-Caputo derivative. We prove the existence and uniqueness of a solution for the FAFDEs. Furthermore, the stability analysis of the model is investigated and the numerical simulation is accordingly performed to support the proposed model. Full article
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Open AccessArticle
Nonlinear Gronwall–Bellman Type Inequalities and Their Applications
Mathematics 2017, 5(2), 31; https://doi.org/10.3390/math5020031 - 31 May 2017
Cited by 2
Abstract
In this paper, some nonlinear Gronwall–Bellman type inequalities are established. Then, the obtained results are applied to study the Hyers–Ulam stability of a fractional differential equation and the boundedness of solutions to an integral equation, respectively. Full article
Open AccessArticle
Discrete-Time Fractional Optimal Control
Mathematics 2017, 5(2), 25; https://doi.org/10.3390/math5020025 - 19 Apr 2017
Cited by 4
Abstract
A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian [...] Read more.
A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian approach. Both the free and fixed final state cases have been considered. Numerical examples are taken up and their solution technique is presented. Results are produced for different values of α . Full article
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