Trends in Mathematics

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2 Trends in Mathematics Trends in Mathematics is a series devoted to the publication of volumes arising from conferences and lecture series focusing on a particular topic from any area of mathematics. Its aim is to make current developments available to the community as rapidly as possible without compromise to quality and to archive these for reference. Proposals for volumes can be submitted using the Online Book Project Submission Form at our website Material submitted for publication must be screened and prepared as follows: All contributions should undergo a reviewing process similar to that carried out by journals and be checked for correct use of language which, as a rule, is English. Articles without proofs, or which do not contain any significantly new results, should be rejected. High quality survey papers, however, are welcome. We expect the organizers to deliver manuscripts in a form that is essentially ready for direct reproduction. Any version of TEX is acceptable, but the entire collection of files must be in one particular dialect of TEX and unified according to simple instructions available from Birkhäuser. Furthermore, in order to guarantee the timely appearance of the proceedings it is essential that the final version of the entire material be submitted no later than one year after the conference. More information about this series at

3 Michael Ruzhansky Yeol Je Cho Praveen Agarwal Iván Area Editors Advances in Real and Complex Analysis with Applications

4 Editors Michael Ruzhansky Department of Mathematics Imperial College London London UK Yeol Je Cho Department of Mathematics Education and the RINS Gyeonsang National University Jinju Korea (Republic of) Praveen Agarwal Department of Mathematics Anand International College of Engineering Jaipur, Rajasthan India Iván Area Departamento de Matemática Aplicada II E.E. Aeronáutica e do Espazo, Universidade de Vigo Ourense Spain ISSN ISSN X (electronic) Trends in Mathematics ISBN ISBN (ebook) DOI / Library of Congress Control Number: Mathematics Subject Classification (2010): 11A15, 30C45, 42A38, 44A10, 46G20, 46E50 Springer Nature Singapore Pte Ltd This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This book is published under the trade name Birkhäuser The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore , Singapore (

5 Contents Certain Image Formulae and Fractional Kinetic Equations Involving Extended Hypergeometric Functions Krunal B. Kachhia, Praveen Agarwal and Jyotindra C. Prajapati The Compact Approximation Property for Weighted Spaces of Holomorphic Mappings Manjul Gupta and Deepika Baweja Bloch Mappings on Bounded Symmetric Domains Tatsuhiro Honda Certain Class of Meromorphically Multivalent Functions Defined by a Differential Operator Ghazi S. Khammash and Praveen Agarwal Bivariate Symmetric Discrete Orthogonal Polynomials Y. Guemo Tefo, Iván Area and M. Foupouagnigni New and Extended Applications of the Natural and Sumudu Transforms: Fractional Diffusion and Stokes Fluid Flow Realms Fethi Bin Muhammed Belgacem, Rathinavel Silambarasan, Hammouch Zakia and Toufik Mekkaoui On Uncertain-Fractional Modeling: The Future Way of Modeling Real-World Problems Abdon Atangana and Ilknur Koca Quadratic Reciprocity and Some Non-differentiable Functions Kalyan Chakraborty and Azizul Hoque Survey on Metric Fixed Point Theory and Applications Yeol Je Cho Sums of Finite Products of Euler Functions Taekyun Kim, Dae San Kim, Gwan Woo Jang and Jongkyum Kwon v

6 vi Contents On a New Extension of Caputo Fractional Derivative Operator İ.O. Kıymaz, P. Agarwal, S. Jain and A. Çetinkaya An Extension of the Shannon Wavelets for Numerical Solution of Integro-Differential Equations Maryam Attary Inverse Source Problem for Multi-term Fractional Mixed Type Equation E.T. Karimov, S. Kerbal and N. Al-Salti

7 About the Editors Michael Ruzhansky is a Professor at the Department of Mathematics, Imperial College London. He has published over 100 research articles in several leading international journals. He has also published five books and memoirs and nine edited volumes. He has researched topics related to pseudo-differential operators, harmonic analysis, and partial differential equations. More recently, he has worked on boundary value problems and their applications. He has been on the editorial board of many respected international journals and served as the President of the International Society of Analysis, Applications, and Computations (ISAAC) in the period Yeol Je Cho is a Professor at the Department of Mathematics Education, Gyeongsang National University, Korea, and Fellow of the Korean Academy of Science and Technology. He has published over 350 research papers in respected international journals, mainly in the field of fixed point theory, variational inequality problems, equilibrium problems, optimization problems, stability of functional equations, and inequality theory. He has been on the editorial boards of several leading journals, such as Fixed Point Theory and Applications, Journal of Nonlinear Science and Applications, and 15 more international journal of mathematics and applications. He has also published a number of remarkable books on fixed point theory, stability of functional equations, numerical analysis, and degree theory. Praveen Agarwal is a Professor at the Department of Mathematics, Anand International College of Engineering, Jaipur, India. He has published over 150 articles related to special functions and fractional calculus in leading mathematics journals, such as Applied Mathematics and Computation, the Journal of Nonlinear Science and Applications, and the Journal of Inequalities and Applications. Recently, he has focused on partial differential equations and fractional differential equations. He has been on the editorial boards of several journals, including SpringerPlus and the Maejo International Journal of Science and Technology. He has been involved in a number of conferences and has also won numerous vii

8 viii About the Editors international research grants such as Research in Group by International Centre for Mathematical Sciences (ICMS) and World Academy of Sciences (TWAS) Visiting Scientist fellowship and many more. Iván Area is a Professor at the Departamento de Matemática Aplicada II, E.E. Aeronáutica e do Espazo Universidade de Vigo, Spain. He has published over 100 articles related to orthogonal polynomials and special functions in leading international journals. His recent research has also focused on fractional analysis and bioinformatics. He has been elected General Secretary of the International Center for Pure and Applied Mathematics (CIMPA), a nonprofit organization whose aim is to promote mathematics in developing countries.