Some general properties of a fractional Sumudu transform in the class of Boehmians

Authors

  • Shrideh K. Qasem Al-Omari Department of Applied Sciences, Faculty of Engineering Technology; Al-Balqa’ Applied University, Amman 11134, Jordan
  • Praveen Agarwal Anand International College of Engineering Jaipur-303012, Rajasthan, India

Keywords:

Boehmian, fractional Sumudu transform, fractional derivative, Mittag- Leffler function, Sumudu transform.

Abstract

In literature, there are several works on the theory and applications of integraltransforms of Boehmian spaces, but fractional integral transforms of Boehmians havenot yet been reported. In this paper, we investigate a fractional Sumudu transform ofan arbitrary order on some space of integrable Boehmians. The fractional Sumudutransform of an integrable Boehmian is well-defined, linear and sequentially completein the space of continuous functions. Two types of convergence are also discussed indetails.

Author Biography

Praveen Agarwal, Anand International College of Engineering Jaipur-303012, Rajasthan, India

 

 

Dr. Praveen Agarwal

(M.Sc., M. Phil., Ph. D)

Associate Professor

 

Bio & Contact Birth (August 18, 1979)
  • Place: Jaipur, Rajasthan, INDIA

 

  • Nationality: India
Address
  • Home: P. No, 3 Maruti Colony, Diggi Malpura Road, Sanganer, Jaipur, Rajasthan India.
    [Postal code: 302029] [Home Phone: +91-141-2732603]
  • Office: Department of Mathematics, Anand International College of Engineering, Jaipur, Near Kanota, Agra Road, Bassi, Jaipur, Rajasthan, India.
    [Postal code: 303012] [Office Phone: +91-9694097809]
  • E-mails: praveen.agarwal@anandice.ac.in goyal.praveen2011@gmail.com
Education
  • Ph.D. in Mathematics, January 2002--August 2006, Rajasthan University, Jaipur
  • M. Phil in Mathematics, July 2001-June 2002, Rajasthan University, Jaipur
  • M.Sc. in Mathematics, July 1998- June 2000, Rajasthan University, Jaipur
  • B.Sc. in Mathematics, July 1995-June 1998, Rajasthan University, Jaipur
Research Interest
  • Broadly: Special Functions, Fractional Calculus, Integral Transform and Mathematical Physics.
Experience Professional Experience

 

  • Associate Professor, July 2010--Present, Anand International College of Engineering Jaipur.
  • Associate Professor, July 2008-- June 2010, Global Institute of Technology, Jaipur.
  • Assistant Professor, July 2005-- June 2008, Global Institute of Technology, Jaipur.
  • Assistant Professor, July 2005-- June 2008, Global Institute of Technology, Jaipur.
  • Guest faculty, Assistant Professor, January 2002-- December 2004, Malviya National Institute of Technology, Jaipur.
Teaching Experience As per rule

 

  • Engineering Mathematics
  • Advanced Engineering Mathematics
  • Higher Engineering Mathematics
  • Operation Research
  • Statistics & Probability Theory
  • Random Variables & Stochastic Processes
Activities Membership of Professional Bodies

 

  • A Member of Who's Who in the World 2014 (31th pearl Anniversary Edition).
  • A Member of Who's Who in the World 2013 (30th pearl Anniversary Edition).
  • A Member of the American Biographical Institute’s prestigious honor “MAN OF THE YEAR 2012”. Of ABI.
  • A Member of “The Cambridge Certificate for Outstanding Educational Achievement” 2012, of IBC.
  • A Member of “2000 Outstanding Intellectuals of the 21st Century 2012” International biographical centre, Cambridge, England.
  • A Member of Governing Body of Anand International College of Engineering 2011.
  • A Member of Who's Who in Science and Engineering 2011-2012 (11th Edition).
  • A Member of Who's Who in the World 2012 (29th Edition).
  • A Life member of the International Association of Engineers, (IAENG/1112298).
  • A Senior member of the International Association of Computer Science and Information Technology.( IACSIT/80345446)
  • A Member of the IAENG Society of Scientific Computing. (IAENG/SSC/ 111229).
  • A Member International Advisory Board of the International Conference on Finite or Infinite Dimensional Complex Analysis and Applications(ICFIDCAA).

 

 

Membership of Mathematical societies

 

  • A Permanent member of “Fractional Calculus and Application Group (FCAG)”.
  • A Life member of “Rajasthan Academy of Physical Sciences”.
  • A Life member of “Society for Special Function and their Applications”.
  • A Life member of “Ramanujan Mathematical Society”.
  • A Senior Member of Science and Engineering institute (SCIEI). (M. No. 20130311002).
  • Member, American Mathematical Society (AMS).

 

 

Experience as a Reviewer and Referee

  • Reviewer: AMS-Mathematical Review (Reviewer No. 90881).
  • Reviewer: Zentralblatt MATH (Reviewer No. 14485).
  • Reviewer:  European Journal of Pure and Applied Mathematics (SCI Journal).
  • Reviewer: Taiwanese Journal of Mathematics, (SCI Journal).
  • Reviewer: Abstract and Applied Analysis, (SCIE Journal).
  • Reviewer: The Scientific World Journal, (SCIE Journal).
  • Reviewer: Mathematical Problems in Engg. , (SCIE Journal).
  • Reviewer: Applied Mathematics and Computation, (SCIE Journal).
  • Reviewer: Boundary Value Problems, (SCIE Journal).
  • Reviewer: JMAA, (SCIE Journal).
  • Reviewer: IMA Journal of Mathematical Control and Information, (SCIE Journal).
  • Acting as a referee for some of the reputed Indian and foreign journal

 

Editorial Board Member in International Journals

  • Editor-in-Chief, International Journal of Mathematical Research (IJMR).
  • Managing Editor, American Journal of Applied Mathematics and Statistics.
  • Managing Editor, American Journal of Mathematical Analysis.
  • Managing Editor, Applied Mathematics and Physics.
  • Chief Technical Advisor, International Journal of Soft Computing and Engineering.
  • Chief Technical Advisor, International Journal of Innovative Sciences and Modern Engineering (IJISME).
  • Technical Editor, Journal of Applied Sciences.
  • Technical Editor, Trends in Applied Sciences Research.
  • Technical Editor, Asian Journal of Scientific Research.
  • Technical Editor, Asian Journal of Mathematics & Statistics.
  • Technical Editor, Asian Journal of Applied Sciences.
  • Member, Editorial Board, South Asian Journal of Mathematics.
  • Member, Editorial Board, Applications and Applied Mathematics.
  • Member, Editorial Board, Pure and Applied Mathematics Journal.
  • Member, Editorial Board, International Journal of Pure Mathematics.
  • Member, Editorial Board, International Journal of Basic, Applied & Social Sciences.
  • Member, Editorial Board, Discovery publication.
  • Member, Editorial Board, Open Journal of Mathematical Modeling.
  • Member, Editorial Board, International Journal of Statistika and Mathematika.
  • Member, Editorial Board, Global Open Research Journal of Mathematics.
  • Member, Editorial Board, International Journal of Physics, Chemistry and Mathematics.
  • Member, Editorial Board, International Journal of Scientific and Innovative Mathematical Research. 
  • Member, Editorial Board, Global Journal of Theoretical and Applied Mathematical Sciences.
  • Member, Editorial Board, American Journal of Mathematics and Statistics.
  • Member, Editorial Board, Asian Journal of Current Engineering & Math’s.
  • Member, Editorial Board, Shiv Shakti International Journal in Multidisciplinary and Academic Research.
  • Member, Editorial Board, World Science Publisher.
  • Member, Editorial Board, International Journal of Engineering and Advanced Technology.
  • Member, Editorial Board, International Journal of Soft Computing and Engineering.
  • Member, Editorial Board, Indian Journal of Engineering.
  • Member, Editorial Board, Indian Journal of Science.
  • Member, Editorial Board, International Journal of Scientific Research and Application.
  • Member, Editorial Board, International Journal of Advance Mathematics and Statistics.
  • Member, Editorial Board, Walaik Journal of Science and Technology.
  • · Member, Editorial Board, International Journal of Scientific and Engineering Research.
  • · Member, Editorial Board, Lecture Notes in Information Science and Technology.
  • Member, Editorial Board, CSCanada Studies in Mathematical Sciences.
  • Member, Editorial Board, Asian Journal of Mathematical Sciences.
  • Member, Editorial Board, International Journal of Advanced Research in Management and Social Sciences.
  • Member, Editorial Board, International Journal of Statistika and Mathematika.
  • Member, International Scientific Committee, International scientific Academy of Engineering & technology.
  • Member, International Scientific Committee, World Congress on Engineering (WCE) 2013,
  • Member, International Scientific Committee, The International Conference of Applied and Engineering Mathematics (ICAEM).

 

 

Guest Editor

 

·                        The Scientific World Journal, Special Issue on “Swarm Intelligence and Its Applications" 2015.

 

  • Abstract and Applied Analysis, Special Issue on “Recent Trends in Fractional Integral Inequalities and their Applications" (FIIA), 2014.

 

  • The Scientific World Journal, Special Issue on “New Trends in Fractional Calculus and Its Applications in Engineering and Other Sciences”, 2014.

 

 

  • Mathematical Problems in Engineering, Special Issue on “Artificial Intelligence and its Applications 2014”.

 

  • The Scientific World Journal, Special Issue on “Swarm Intelligence and Its Applications”, 2014.

 

  • The Scientific World Journal, Special Issue on “Swarm Intelligence and Its Applications”, 2013.

  • Mathematical Problems in Engineering, Special Issue on “Artificial Intelligence and Its Applications”, 2013

Visits to Foreign Countries

 

 

  • Invited by the International Congress of Mathematics(ICM-2014), Republic of Korea, to present a Poster at the International Congress of Mathematics(ICM-2014), held from 13-21 August 2014 at Seoul, Republic of Korea.

 

  • Invited by the Professor Junesang Choi, Department of Mathematics, Dongguk University, Republic of Korea, to give a talk  at the 22ndInternational Conference on Finite or Infinite Dimensional Complex Analysis and Applications(ICFIDCAA)held from 8-11 August 2014 in the Mathematics Department of Dongguk University, Republic of Korea.

  • Invited by IMA (Institute for Mathematics and their Applications), University of Minnesota, Minneapolis, USA, to presented a poster at the IMA Annual Program Year Workshop on “Algebraic Topology in Dynamics, Differential Equations, and Experimental Data held on February 10-14, 2014 in IMA.

 

  • Invited by The Professor Junesang Choi, Department of Mathematics, Dongguk University, Republic of Korea, for 10 days during January and February of 2013 in order to talk about and work the common research parts

 

  • Invited by TOBB University of Economics and Technology in Ankara, to give a talk at the International Conference on Applied Mathematics & Approximation Theory, (AMAT 2012) held from 17-20 May 2012 in the TOBB University of Economics and Technology in Ankara, (Turkey).

 

Award of Fellowships and Gold Medals

 

  • Selected for the UNESCO-IRAK SCHOOL (CIMPA) on "Inverse problems: Theory and applications" held at Erbil, May 5, 2014 - May 14, 2014.
  • ·
  • Awarded an IASc-INSA-NASI Summer Research Fellowship in 2014. The fellowship to work for two months during this summer.  I will be working with Dr Amit P. Kesarkar, National Atmospheric Research Laboratory, Tirupati (e-mail: amit.kesarkar@gmail.com).

 

  • Awarded the NANUM 2014 Travel Grants from SEOUL ICM 2014, to attend the International Congress of Mathematicians 2014, held from August 13 - 21, 2014, Seoul, Korea.

 

  • Awarded the International Travel Grant from National Board for Higher Mathematics, (NBHM), to attend the IMA Annual Program Year Workshop on “Algebraic Topology in Dynamics, Differential Equations, and Experimental Data held on February 10-14, 2014 in IMA (Institute for Mathematics and their Applications), University of Minnesota, Minneapolis, USA.

 

  • Awarded the International Travel Grant from Human Resource Development Group Council of Scientific & Industrial Research (CSIR), to attend International Congress on Honor of Prof. H.M.Srivastava 2012 held from 23-26 July 2012 in the Uldag University, Bursa, (Turkey).

 

  • Awarded the International Travel Grant from Ministry of Science and Technology, Department of Science and Technology Government of India (ITS) to attend International Conference on Applied Mathematics & Approximation Theory, AMAT 2012 held from 17-20 May 2012 in the TOBB University of Economics and Technology in Ankara, (Turkey).

 

  • Awarded Research Fellowship from Malviya National Institute of Technology of Jaipur for three years during the session 2002-2004. Esteemed

Invited talk in Seminar/Conferences/STTP/QIP

  • Invited by the International Congress of Mathematics(ICM-2014), Republic of Korea, to present a Poster at the International Congress of Mathematics(ICM-2014), held from 13-21 August 2014 at Seoul, Republic of Korea.

 

  • Invited by the Professor Junesang Choi, Department of Mathematics, Dongguk University, Republic of Korea, to give a talk  at the 22ndInternational Conference on Finite or Infinite Dimensional Complex Analysis and Applications(ICFIDCAA)held from 8-11 August 2014 in the Mathematics Department of Dongguk University, Republic of Korea.
  • International Conference on “International Conference on Special Functions & Applications (ICSFA 2013) & Symposium on Applications in diverse fields of Engineering and Technology, held at Department of Mathematics, Malviya National Institute of Technology, Jaipur from December 13-15, 2013.
  • Invited by Indian Institute of Science, Bangalore, to participate at the Conference in Honour of Sixth Birthday of Rajendra Bhatiya held from 27-30 December 2012 in the Mathematics Department of Indian Institute of Science, Bangalore (INDIA).

 

  • Invited by University of Delhi, Delhi, to participate at the International Conference in Honour of Ramanujan of title "The Legacy of Srinivasa Ramanujan" to be organized by the University of Delhi during Dec 17-22, 2012.  (INDIA).

 

  • International Conference on Applied Mathematics & Approximation Theory, (AMAT 2012) held from 17-20 May 2012 in the TOBB University of Economics and Technology in Ankara, (Turkey).
  • International Conference On Special Functions  &Their Applications (ICSF 2011) & Symposium on Works of Ramanujan (Xth Annual Conference of SSFA) to be held in Department of Mathematics & Statistics, J. N. Vyas University, Jodhpur (Rajasthan), India, from July 28-30, 2011.
  • "Workshop on Ramanujan's Mathematics" to be held in The National Academy of Sciences India, Allahabad from December 22-24, 2010.
  • National Conference on Advances in Wireless and Optical Communication Technologies2010 to be held in Poornima College of Engineering, Jaipur from August 7-8, 2010.
  • 21st National Conference of Rajasthan Ganita Parishad on Recent Trends in Mathematics & Actuarial Sciences held at Department of Mathematics, Malviya National Institute of Technology, Jaipur from February 20 - 21, 2010
  • National Conference on “Recent Developments in Engineering Mathematics & Information Technology” held at Department of Mathematics, Poornima College of Engineering, Jaipur from December 25-26, 2009.
  • Workshop on Developing Core Teaching and Learning Competencies, held at Global Institute of Technology,  Jaipur from June 8-13, 2009.
  • International Conference on “Special Functions and their Engineering Applications” ” held at Department of Mathematics, Malviya National Institute of Technology, Jaipur from December 15-16, 2007.
  • Workshop on Enrichment of Teaching-Learning Skills, held at Global Institute of Technology,  Jaipur from December 13-15, 2007.
  • 12th Annual Conference of Vijnana Perished of India and National Symposium on Applications of Special Functions organized by the Dept. of Mathematics & Statistics, Jai Narain Vyas University Jodhpur, Rajasthan, India, between October 25-27, 2007.
  • AICTE-STAFF Development Programme on “Application Orientation in Engineering Mathematics” ” held at Department of Mathematics, Malviya National Institute of Technology, Jaipur from June 25th to July 6th 2007.
  • International Conference on “Advanced Manufacturing Technologies” held at Jagan Nath Gupta Institute of Technology, Jaipur from December 15, 2006.
  • International Conference on “Special Functions and their Applications” ” held at Department of Mathematics, University of Pune, and Maharastra from February 21-23, 2006.
  • 4th Annual Conference of “Society for Special Functions and their Applications” held at Department of Mathematics, University of Rajasthan, Jaipur from February 20-22, 2003.
Publications Books
  • P. Agarwal, A Study of New Trends and Analysis of Special Function LAP LAMBERT Academic Publishing is a trademark of: AV Akademikerverlag GmbH & Co. KG ( ISBN 978-3-659-312861).

 

  • P. Agarwal, Engineering Mathematics-I, Published in Paragon International Publishers, New Delhi, 2007.

  • P. Agarwal and S. Jain, Advanced Mathematics (EC, EIC, EE) Published in Paragon International Publishers, New Delhi, 2008.

 

  • P. Agarwal and S. Jain, Advanced Engineering Mathematics-IV, Published in Nandani Prakashan Pvt. Ltd., 2011.

Research Papers

 

  1. 1. G. Wang, P. Agarwal and D. Baleanu, Certain new Gruss type inequalities involving Saigo fractional q-integral operator, J. Computational Analysis and Application. (Accepted). (I.F. :0.72)

  1. 2. J. C. Prajapati, N. K. Ajudia, P. Agarwal, Some Results due to Konhauser Polynomials of First Kind and Laguerre Polynomials, Applied Mathematics and Computation. (Accepted). (I.F.:1.6)

  1. 3. H.M.Srivastava, P. Agarwal and S.Jain, Generating Functions for the Generalized Gauss  Hypergeometric Functions, Applied Mathematics and Computation. (Accepted). (I.F.:1.6)

  1. 4. S. Salahshour, A. Ahmadian, C.S. Chan, D. Baleanu and P. Agarwal, On Exact Solutions of Fuzzy Fractional Differential Equation with Uncertainty, Abstract and Applied Analysis. (Accepted). (I.F.:1.274)

  1. 5. J. Choi , Praveen Agarwal and S. Jain, Certain fractional integral operators and extended generalized Gauss hypergeometric functions, Kyungpook Mathematical Journal. (Accepted).

5.

  1. 6. S. Salahshour, A. H. Bhrawy, Praveen Agarwal, A. Ahmadian, N. Senu, A. K. Shukla and R. K. Jana, Integrals containing Laguerre-type Polynomials and Bessel functions, Abstract and Applied Analysis. (Accepted). (I.F.:1.274)

  1. 7. J. Choi, Praveen Agarwal, Certain integral transforms for the incomplete functions, Applied Mathematics & Information Sciences (Accepted). (I.F.: 1.232).

 

  1. D. Baleanu and Praveen Agarwal, A Compositions Formula of the Pathway Integral Transforms Operator, Note di Matematica (Accepted).

 

  1. 9. Praveen Agarwal, S. Jain, Saket Dwivedi, A new class of integral relations involving general class of Polynomials and I-functions, Walailak J. Sci. & Tech. (Accepted). (I.F.: 0.14).

10. Praveen Agarwal, M. Chand and S.D. Purohit, A note of generating functions involving the generalized Gauss hypergeometric functions, Nat. Academy Sci. Letters (Accepted). (I.F.: 0.07).

11. Praveen Agarwal, S.Salahshour, S. K. Ntouyas and J. Tariboon, Certain inequalities involving generalized Erdelyi-Kober fractional q-integral operators. The Scientific World Journal, Volume 2014, Article ID 174126, 11 pages. . (I.F.: 1.73).

12. J. Choi , Praveen Agarwal, Certain class of generating functions for the incomplete hypergeometric functions, Abstract and Applied Analysis, Volume 2014, Article ID 714560, 5 pages(I.F.:1.274)

13. D. Kumar, Praveen Agarwal and S.D. Purohit, Generalized fractional integration of the H-function involving general class of polynomials, Walailak J. Sci. & Tech. 11, 2014. (I.F.: 0.14).

14. J. Choi , Praveen Agarwal, S.  Mathur and S. D. Purohit, Certain new integral formulas involving the generalized Bessel functions, Bull. Korean Math. Soc. 51(4) (2014), 995–1003. (I.F.: 0.448).

 

15.  J. Choi and Praveen Agarwal, Certain fractional integral inequalities involving hypergeometric operators, East Asian Math. J. 30(3) (2014), 283-291.

 

16.  J. Choi and Praveen Agarwal, Certain new Pathway type fractional integral inequalities, Honam Mathematical J. 36(2) (2014), 437-447.

 

17.  P. Agarwal, S. Jain, S. Agarwal, M. Nagpal, On a new class of integrals involving Bessel functions of the first kind, Communications in Numerical Analysis, 2014 (2014) 1-7.

 

 

18. J. Choi and Praveen Agarwal , Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions, Abstract and Applied Analysis (2014), 2014/ 735946. (I.F.:1.274)

 

 

19.  D. Baleanu and Praveen Agarwal, On Generalized Fractional Integral Operators and the generalized Gauss hypergeometric Functions, Abstract and Applied Analysis (2014), 2014/ 630840. . (I.F.:1.274)

20. D. Baleanu and Praveen Agarwal, Certain inequalities involving the fractional q-integral operators, Abstract and Applied Analysis (2014), 2014/371274. . (I.F.:1.274).

21. J. Choi and P. Agarwal, Some new Saigo type fractional integral inequalities and their q-analogues, Abstract and Applied Analysis (2014), 2014/579260. . (I.F.:1.274)

22.  Praveen Agarwal, J. Tariboon, S. Jain, New Bilateral Type Generating Function Associated with

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Published

09-05-2016

Issue

Vol. 43 No. 2 (2016): Kuwait Journal of Science

Section

Mathematics