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axioms Mathematical Analysis and Applications Edited by Hari Mohan Srivastava Printed Edition of the Special Issue Published in Axioms www.mdpi.com/journal/axioms Mathematical Analysis and Applications Mathematical Analysis and Applications Special Issue Editor Hari Mohan Srivastava MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editor Hari Mohan Srivastava University of Victoria Canada Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Axioms (ISSN 2075-1680) in 2018 (available at: https://www.mdpi.com/journal/axioms/special issues/ mathematical analysis) For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03897-400-0 (Pbk) ISBN 978-3-03897-401-7 (PDF) c 2019 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editor ...................................... vii H. M. Srivastava Mathematical Analysis and Applications Reprinted from: Axiomss 2018, 7, 82, doi:10.3390/axioms7040082 ................... 1 Pierpaolo Natalini and Paolo Emilio Ricci New Bell–Sheffer Polynomial Sets Reprinted from: Axiomss 2018, 7, 71, doi:10.3390/axioms7040071 ................... 3 Makrina Agaoglou, Michal Feˇckan, Michal Posp´ısil,ˇ Vassilis M. Rothos and Alexander F. Vakakis Periodically Forced Nonlinear Oscillatory Acoustic Vacuum Reprinted from: Axiomss 2018, 7, 69, doi:10.3390/axioms7040069 ................... 13 Chenkuan Li, Thomas Humphries and Hunter Plowman Solutions to Abel’s Integral Equations in Distributions Reprinted from: Axiomss 2018, 7, 66, doi:10.3390/axioms7030066 ................... 26 Jean-Daniel Djida and Arran Fernandez Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions Reprinted from: Axiomss 2018, 7, 65, doi:10.3390/axioms7030065 ................... 43 Giuseppe Dattoli, Bruna Germano, Silvia Licciardi, Maria Renata Martinelli Umbral Methods and Harmonic Numbers Reprinted from: Axiomss 2018, 7, 62, doi:10.3390/axioms7030062 ................... 59 Nonthamon Chaikham and Wannika Sawangtong Sub-Optimal Control in the Zika Virus Epidemic Model Using Differential Evolution Reprinted from: Axiomss 2018, 7, 61, doi:10.3390/axioms7030061 ................... 68 Taekyun Kim and Cheon Seoung Ryoo Some Identities for Euler and Bernoulli Polynomials and Their Zeros Reprinted from: Axiomss 2018, 7, 56, doi:10.3390/axioms7030056 ................... 82 Hafize G ¨um¨u¸s and Nihal Demir A New Type of Generalization on W —Asymptotically Jλ—Statistical Equivalence with the Number of α Reprinted from: Axiomss 2018, 7, 54, doi:10.3390/axioms7030054 ...................101 Konstantin Zhukovsky, Dmitrii Oskolkov and Nadezhda Gubina Some Exact Solutions to Non-Fourier Heat Equations with Substantial Derivative Reprinted from: Axiomss 2018, 7, 48, doi:10.3390/axioms7030048 ...................112 Mohammad Masjed-Jamei and Wolfram Koepf Some Summation Theorems for Generalized Hypergeometric Functions Reprinted from: Axiomss 2018, 7, 38, doi:10.3390/axioms7020038 ...................130 Hsien-Chung Wu Pre-Metric Spaces Along with Different Types of Triangle Inequalities Reprinted from: Axiomss 2018, 7, 34, doi:10.3390/axioms7020034 ...................150 v Antti Rasila and Tommi Sottinen Yukawa Potential, Panharmonic Measure and Brownian Motion Reprinted from: Axiomss 2018, 2, 28, doi:10.3390/axioms7020028 ...................160 Hanaa M. Zayed, Mohamed Kamal Aouf and Adela O. Mostafa Subordination Properties for Multivalent Functions Associated with aGeneralized Fractional Differintegral Operator Reprinted from: Axiomss 2018, 7, 27, doi:10.3390/axioms7020027 ...................173 Omer¨ Ki¸si,Hafize G ¨um¨u¸s and Ekrem Savas I New Definitions about A -Statistical Convergence withRespect to a Sequence of Modulus Functions and Lacunary Sequences Reprinted from: Axiomss 2018, 7, 24, doi:10.3390/axioms7020024 ...................186 Yilmaz Simsek Special Numbers and Polynomials Including TheirGenerating Functions in Umbral Analysis Methods Reprinted from: Axiomss 2018, 7, 22, doi:10.3390/axioms7020022 ...................198 vi About the Special Issue Editor Hari Mohan Srivastava has held the position of Professor Emeritus in the Department of Mathematics and Statistics at the University of Victoria in Canada since 2006, having joined the faculty there in 1969, first as an Associate Professor (1969–1974) and then as a Full Professor (1974–2006). He began his university-level teaching career right after having received his M.Sc. degree in 1959 at the age of 19 years from the University of Allahabad in India. 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. He has held numerous visiting research and honorary chair positions at many universities and research institutes in different parts of the world. Having received several D.Sc. (honoris causa) degrees as well as honorary memberships and honorary fellowships of many scientific academies and learned societies around the world, he is also actively associated editorially with numerous international scientific research journals. His current research interests include several areas of Pure and Applied Mathematical Sciences, such as 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 Modelling and Optimization. He has published 27 books, monographs, and edited volumes, 30 book (and encyclopedia) chapters, 45 papers in international conference proceedings, and more than 1100 scientific research articles in peer-reviewed international journals, as well as forewords and prefaces to many books and journals, and so on. He is a Clarivate Analytics [Thomson-Reuters] (Web of Science) Highly Cited Researcher. For further details about his other professional achievements and scholarly accomplishments, as well as honors, awards, and distinctions, including the lists of his most recent publications such as journal articles, books, monographs and edited volumes, book chapters, encyclopedia chapters, papers in conference proceedings, forewords to books and journals, et cetera), the interested reader should look into the following regularly updated website. vii Editorial Mathematical Analysis and Applications Hari M. Srivastava 1,2 1 Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada; [email protected] 2 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan Received: 7 November 2018; Accepted: 7 November 2018; Published: 12 November 2018 Website: http://www.math.uvic.ca/faculty/harimsri/ This volume contains the invited, accepted and published submissions (see [1–15]) to a Special Issue of the MDPI journal Axioms on the subject-area of “Mathematical Analysis and Applications”. In recent years, investigations involving the theory and applications of mathematical analytic tools and techniques have become remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications. The suggested topics of interest for the call for papers of this Special Issue included, but were not limited to, the following keywords: • Mathematical (or Higher Transcendental) Functions and Their Applications • Fractional Calculus and Its Applications • q-Series and q-Polynomials • Analytic Number Theory • Special Functions of Mathematical Physics and Applied Mathematics • Geometric Function Theory of Complex Analysis Here, in this Editorial, we briefly describe the status of the Special Issue as follows: 1. Publications: 15; 2. Rejections: 24; 3. Article Average Processing Time: 52 days; 4. Article Type: Research Article (15); Review (0); Correction (0) Authors’ geographical distribution: • Italy (6) • Turkey (5) • Egypt (3) • Russian Federation (3) • Canada (2) • Korea (2) • Finland (2) • Thailand (2) • Slovakia (2) • Spain (1) • Iran (1) Axioms 2018, 7, 82; doi:10.3390/axioms70400821 www.mdpi.com/journal/axioms Axioms 2018, 7,82 • Taiwan (Republic of China) (1) • Germany (1) • Greece (1) • UK (1) • USA (1) References 1. Natalini, P.; Ricci, P.E. New Bell–Sheffer polynomial sets. Axioms 2018, 7, 71, doi:10.3390/axioms7040071. [CrossRef] 2. Agaoglou, M.; Feˇckan, M.; Pospíššil, M.; Rothos, V.M.; Vakakis, A.F. Periodically forced nonlinear oscillatory acoustic vacuum. Axioms 2018, 7, 69, doi:10.3390/axioms7040069. [CrossRef] 3. Li, C.-K.; Humphries, T.; Plowman, H. Solutions to Abel’s integral equations in
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