Special Issue "Differential and Difference Equations: A Themed Issue Dedicated to Prof. Hari M. Srivastava on the Occasion of his 80th Birthday"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 31 May 2020.

Special Issue Editor

Prof. Dr. Sotiris K. Ntouyas
E-Mail Website
Guest Editor
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Interests: initial and boundary value problems for differential equations and inclusions; inequalities
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Special Issue Information

Dear Colleagues,

This Special Issue of Axioms is dedicated to Professor Hari Mohan Srivastava on the occasion of his 80th Birthday, as recognition of his significant contribution in the field.

Hari Mohan Srivastava was born on 05 July 1940 in Karon (District Ballia) in the Province of Uttar Pradesh in India. Professor Hari Mohan Srivastava began his university-level teaching career right after having received his M.Sc. degree in 1959 at the age of 19 years. He earned his Ph.D. degree in 1965 while he was a full-time member of the teaching faculty at the Jai Narain Vyas University of Jodhpur in India (since 1963). Currently, Professor Srivastava holds the position of Professor Emeritus in the Department of Mathematics and Statistics at the University of Victoria in Canada, having joined the faculty there in 1969. Professor Srivastava has held (and continues to hold) numerous Visiting and Chair Professorships at many universities and research institutes in many different parts of the world. Having received several D.Sc. (honoris causa) degrees as well as honorary memberships and fellowships of many scientific academies and scientific societies around the world, he is also actively associated editorially with numerous international scientific research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited (and is currently editing) many Special Issues of scientific research journals as the Lead Guest Editor, including (for example) the MDPI journals Axioms, Mathematics, and Symmetry, the Elsevier journals Journal of Computational and Applied Mathematics and Applied Mathematics and Computation, the Wiley journal Mathematical Methods in the Applied Sciences, and so on. He is a Clarivate Analytics [Thomson Reuters] (Web of Science) Highly-Cited Researcher.

Professor Srivastava’s research interests include several areas of pure and applied mathematical sciences, such as (for example) 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, and inventory modeling and optimization. He has published 33 books, monographs, and edited volumes, 33 book (and encyclopedia) chapters, 48 papers in international conference proceedings, and more than 1200 peer-reviewed international scientific research journal articles, as well as Forewords and Prefaces to many books and journals.

Further details about Professor Srivastava’s professional achievements and scholarly accomplishments, as well as honors, awards and distinctions, can be found at the following website:
http://www.math.uvic.ca/~harimsri/

Differential and difference equations play an important role in many branches of mathematics. This Special Issue deals with the theory and applications of differential and difference equations. We invite high-quality original research papers, as well as survey papers related to the topic of this issue.

We look forward to your contributions.
Best wishes,

Prof. Dr. Sotiris K. Ntouyas
Guest Editor

Manuscript Submission Information

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Keywords

  • ordinary differential equations
  • difference equations
  • partial differential equations
  • fractional differential equations
  • stochastic differential equations
  • time scale dynamic equations
  • related topics about the differential equations

Published Papers (4 papers)

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Research

Open AccessArticle
General Linear Recurrence Sequences and Their Convolution Formulas
Axioms 2019, 8(4), 132; https://doi.org/10.3390/axioms8040132 (registering DOI) - 19 Nov 2019
Abstract
We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 1 1 + a t + b t 2 x . The case of generating functions containing [...] Read more.
We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 1 1 + a t + b t 2 x . The case of generating functions containing parameters, even in the numerator is considered. Convolution formulas and general recurrence relations are derived. Many illustrative examples and a straightforward extension to the case of matrix polynomials are shown. Full article
Open AccessArticle
Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches
Axioms 2019, 8(4), 125; https://doi.org/10.3390/axioms8040125 - 07 Nov 2019
Abstract
The fractional traveling wave solution of important Whitham–Broer–Kaup equations was investigated by using the q-homotopy analysis transform method and natural decomposition method. The Caputo definition of fractional derivatives is used to describe the fractional operator. The obtained results, using the suggested methods are [...] Read more.
The fractional traveling wave solution of important Whitham–Broer–Kaup equations was investigated by using the q-homotopy analysis transform method and natural decomposition method. The Caputo definition of fractional derivatives is used to describe the fractional operator. The obtained results, using the suggested methods are compared with each other as well as with the exact results of the problems. The comparison shows the best agreement of solutions with each other and with the exact solution as well. Moreover, the proposed methods are found to be accurate, effective, and straightforward while dealing with the fractional-order system of partial differential equations and therefore can be generalized to other fractional order complex problems from engineering and science. Full article
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Open AccessArticle
On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order
Axioms 2019, 8(4), 117; https://doi.org/10.3390/axioms8040117 - 18 Oct 2019
Abstract
The present paper is devoted to the spectral analysis of operators induced by fractional differential equations and boundary conditions of Sturm-Liouville type. It should be noted that these operators are non-self-adjoint. The spectral structure of such operators has been insufficiently explored. In particular, [...] Read more.
The present paper is devoted to the spectral analysis of operators induced by fractional differential equations and boundary conditions of Sturm-Liouville type. It should be noted that these operators are non-self-adjoint. The spectral structure of such operators has been insufficiently explored. In particular, a study of the completeness of systems of eigenfunctions and associated functions has begun relatively recently. In this paper, the completeness of the system of eigenfunctions and associated functions of one class of non-self-adjoint integral operators corresponding boundary value problems for fractional differential equations is established. The proof is based on the well-known Theorem of M.S. Livshits on the spectral decomposition of linear non-self-adjoint operators, as well as on the sectoriality of the fractional differentiation operator. The results of Dzhrbashian-Nersesian on the asymptotics of the zeros of the Mittag-Leffler function are used. Full article
Open AccessArticle
Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function
Axioms 2019, 8(4), 112; https://doi.org/10.3390/axioms8040112 - 11 Oct 2019
Abstract
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new families, but also derive many new [...] Read more.
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new families, but also derive many new identities, relations, derivative formulas, and combinatorial sums with the inclusion of binomials coefficients, falling factorial, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), the Poisson–Charlier polynomials, combinatorial numbers and polynomials, the Bersntein basis functions, and the probability distribution functions. Furthermore, by applying the p-adic integrals and Riemann integral, we obtain some combinatorial sums including the binomial coefficients, falling factorial, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), and the Cauchy numbers (or the Bernoulli numbers of the second kind). Finally, we give some remarks and observations on our results related to some probability distributions such as the binomial distribution and the Poisson distribution. Full article
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