Generalized fractional integration of the \overline{H}-function

Authors

  • Praveen Agarwal Dr. Praveen Agarwal Associate Professor of Mathematics & Head of Department Anand International College of Engineering Near Kanota, Agra Road Jaipur -302012 Contact No.: 91-9461664741

Keywords:

Fractional integral operators by Saigo-function, generalized Riemann-Liouville, Erdelyi-Kober, Generalized Wright hypergeometric function, Generalized Wright-Bessel function, The polylogarithm and Mittag-Leffler functions, General class of polynomials

Abstract

A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). In the present paper, we study and develop the generalized fractional integral operators given by Saigo. First, we establish two Theorems that give the images of the product of H-function and a general class of polynomials in
Saigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known Images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings.

Author Biography

  • Praveen Agarwal, Dr. Praveen Agarwal Associate Professor of Mathematics & Head of Department Anand International College of Engineering Near Kanota, Agra Road Jaipur -302012 Contact No.: 91-9461664741

    NAME                    :  Dr. PRAVEEN AGARWAL

    DATE OF BIRTH     :  August 18, 1979

    FATHER’S NAME   :  Dr. N. K. AGARWAL

    TELEPHONE NO.   :  0141-2732603

    MOBLIE NO.           : 91-9461664741

    EMAIL                      : goyal_praveen2000@yahoo.co.in

    &

    goyal_praveen2000@rediffmail.com   

    RESIDENTIAL ADDRESS: Plot No.3, Maruti Colony,

    Diggi Malpura Road,

    Sanganer, Jaipur-302029(Raj.), INDIA

     

    NATIONALITY       : INDIAN

    EDUCATIONAL QUALIFICATIONS

     

    Examination/Degree

    Board/ University

    Subject/ Specialization

    Year of Passing

    Secondary  Examination

    Rajasthan Board

    All

    1993

    Senior Secondary Examination

    Rajasthan Board

    PCM

    1995

    B.Sc.

    Rajasthan University

    PCM

    1998

    M.Sc.

    Rajasthan University

    Mathematics

    2000

    M.Phil.

    Rajasthan University

    Mathematics

    2002

    Ph.D

    Rajasthan University

    SPECIAL FUNCTIONS

    2006

     

    1. 1. Topic of Ph. D.: Investigations in Generalized Laplace Transform Special Functions and Fractional Calculus.
    2. 2. Topic of M. Phil: A Study of Convolution Integral Equations.
    3. 3. Fifteen Research Publications in International & National Journals, Two Research Papers are accepted for the Publication and Ten Research Papers are communicated for Publication.
    4. 4. One research project entitled “A Study of fractional calculus (Derivatives and Integrals to an arbitrary order) and Mellin-Barnes Integral with applications” submitted to All India Council of Technical Education, New Delhi.
    5. 5. One student Guided for Ph.D. “Mr.  Mehar Chand Lecturer in B.R. Mahindra Poly-technical College, Talwandi Sabo-151302, India”

     

    PROFESSIONAL EXPERIENCES

    1. Research Scholar, January  2002 under the supervision of  Prof. C. L. Koul in Malviya National Institute of Technology, Department of Mathematics, Jaipur, India
    2. Registered for Ph.D.,December 2002 on the Topic “Investigations In                  Generalized Laplace Transform, Fraction Calculus and Special Functions” in Rajasthan University, Jaipur, India
    3. Lecturer (Guest faculty), Department of Mathematics, Malviya National Institute of Technology, Jaipur.From November 2002 to December2005.
    4. Lecturer (Sr. Lecturer), Department of Mathematics, Global Institute of Technology (GIT), Sitapura, Jaipur, From July’2005 to June 2007.
    5. Associate Professor Department of Mathematics, Global Institute of Technology (GIT), Sitapura, Jaipur, From July 2007 to July 2010.
    6. Asst. Superintendent: Asst. Superintendent of Examination, Global Institute of Technology (GIT), Sitapura, Jaipur, From July 2008 to July 2010.
    7. Coordinator of   Transportation: Global Institute of Technology (GIT), Sitapura, Jaipur, From July 2005 to July 2010.
    8. Coordinator of   Alumni Association: Global Institute of Technology (GIT), Sitapura, Jaipur, From December 2007 to July 2010..
    9. Coordinator “Department of Applied Sciences and Humanities” Global Institute of Technology (GIT), Sitapura, Jaipur, From July 2005 to July 2010.

    10.  Research Guide, Appoint as a Research Guide in Sighania University, since July 2010.

    11.  Research Guide & Visiting Faculty, Appoint as a Research Guide and Visiting Faculty in Dr. K. N. Modi University, Newai (Rajasthan), Since June 2011. (DKNMU/SC/11-60).

    12.  Technical Editors, Appoint as a member of Technical editorial team of Asian Journal of Mathematics & Statistics & Asian Journal of Applied Sciences, Science January 2012.

    13.  Associate Professor, Department of Mathematics, Anand International College of Engineering, Jaipur; Since August 2010 to till date.

    14.  Operation Manager, Anand International College of Engineering, Jaipur; Since January 2011 to June 2011.

    15.  HOD “Department of Mathematics" Anand International College of Engineering, Jaipur; Since August 2010 to till date.

    16.  Coordinator of   Transportation: Anand International College of Engg., Jaipur, Since August’2010 to till date.

     

    WORK EXPERINCE

     

    • 4 yers Reviewer experience in various International Journals like Asian-European Journal of Mathematics, European Journal of Pure and Applied Mathematics, Journal of Mathematical Research, Tamkong Journal of Mathematics Korian Journal of Mathematics etc.
    • 11yrs Research experience.
    • 11yrs Academic and Administrative experience.
    • Member of different committees constituted for the progress of College (Academic, Examination, Cultural, Discipline, and Timetable).
    • Coordinator of Examination 5years experience.
    • Coordinator of Transportations 6 year’s experience.
    • Coordinator “ Department of Applied Sciences and Humanities” 5years experience
    • Coordinator of Alumni Committee 4years experience.

     

    SUBJECTS TAUGHT IN BE DEGREE COURSES

    BE I year-I Sem.

    1. 1. Engineering Mathematics-I

    BE I year-II Sem.

    1. 2. Engineering Mathematics-II

    BE II year-III Sem.

    3. Engineering Mathematics-III

    (All Branches)

    BE II year-IV Sem

    4. Advanced Mathematics

    (E&C, EIC, EE)

    BE III year-V Sem. (Computer Engineering), VI Sem. (IT)

    5. Optimization Technique

    6. Statistics and Probability

    BE IV year-VII Sem. (Mechanical Engg.)

    7. Operation Research

    8. Q.T. (MBA)

     

     

     

     

    DISTINCTION/PRIZES

    • Ø Caption of the Winner Cricket Team in M.Sc.2000.
    • Ø Distinction in Mathematics B.Sc. Examination 1996.
    • Ø Distinction in Mathematics Secondary Examination 1993.
    • Ø Participation in Cultural activities at school level. Won several prizes

     

    FIELDS OF INTEREST

    • Fractional Calculus
    • Operation Research
    • Advanced Mathematics
    • Numerical Analysis
    • Geometry Theory

    INTERANATIONAL /NATIONAL CONFERENCES/WORKSHOP/SYMPOSIA

    1. INTERNATIONAL CONFERENCE ON SPECIAL FUNCTIONS &THEIR APPLICATIONS (ICSFA 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.
    2. "Workshop on Ramanujan's Mathematics" to be held in The National Academy of Sciences India, Allahabad from December 22-24, 2010.
    3. NATIONAL CONFERENCE ON ADVANCES IN WIRELESS AND OPTICAL COMMUNICATION TECHNOLOGIES-2010 to be held in Poornima College of Engineering, Jaipur from August 7-8, 2010.
    4. 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
    5. 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.
    6. Workshop on Developing Core Teaching and Learning Competencies, held at Global Institute of Technology,  Jaipur from June 8-13, 2009.
    7. 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.
    8. Workshop on Enrichment of Teaching-Learning Skills, held at Global Institute of Technology,  Jaipur from December 13-15, 2007.
    9. 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.

    10.  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.

    11.  International Conference on “Advanced Manufacturing Technologies” held at Jagan Nath Gupta Institute of Technology, Jaipur from December 15, 2006.

    12.  International Conference on “Special Functions and their Applications” ” held at Department of Mathematics, University of Pune, and Maharastra from February 21-23, 2006.

    13.  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.

    MEMBER OF NATIONAL AND INTERNATIONAL SOCIETY

    1. Member of Technical Editorial team of Asian Journal of Mathematics & Statistics and Asian Journal of Applied Sciences, 2012.
    2. Member of Governing Body of Anand International College of Engineering 2011.
    3. Member of Who's Who in Science and Engineering 2011-2012 (11th Edition).
    4. Member of Who's Who in the World 2012 (29th Edition).
    5. Life member of the International Association of Engineers (IAENG).
    6. Life member of “Rajasthan Academy of Physical Sciences”.
    7. Life member of “Society for Special Function and their Applications”.

    LIST OF PUBLICATIONS

    1. P. Agarwal and C.L. Koul, On Generating Functions, J.Rajasthan Acad.Phy.Sci., Vol.2, No.3, 2003, pp.173-180.
    2. P. Agarwal and C.L. Koul, Summation Formulae Involving F, Ganita Sandesh Vol.18, No.2, 2004 pp.125-132.
    3. P. Agarwal and C.L. KouI, Integrals involving product of H and the generalized polynomials , Proc.Nat.Acad.Sci.India, 74(A), IV, 2004.
    4. P. Agarwal and C.L. Koul, Relations Involving -Functions and H-functions, South East Asian J.Math. & Math.Sc.Vol.3 No.2, 2005, pp.1-8.
    5. P. Agarwal and C.L. Koul, Relations Involving -Functions and H-functions of Several Variables, J. Indian Acad. Math. 28, No. 1, 63-72 (2006).
    6. P. Agarwal, On Certain Functional Relations, Bull.Pure.and Appl.Math.Vol.2, No.2, December 2008, pp.199-205.
    7. P.Agarwal and S.Jain, On unified finite integrals involving a multivariable polynomial and a generalized Mellin Barnes type of contour integral having general argument, National Academy   Science Letters, Vol.32, No.8 & 9, 2009.
    8. P.Agarwal, S.Jain and M. Chand, NEW INTERGRAL FORMULAS INVOLVING POLYNOMIALS AND I-FUNCTIO, Proc. of Math. Soc., B.H.U. vol.26 (2010), pp. 61-68.
    9. P.Agarwal and S.Jain , A New Basic Integral Formula Involving General Sequence of Functions, Proceeding of NCAWOCT-2010,Jaipur .
    10. P.Agarwal and S.Jain, On Integrals involving product of H,  and  , Rev.Bull.Cal.Math.Soc.,18,(1),2010,pp. 13-20.
    11. P.Agarwal, S.Jain and M. Chand, Integrals involving product of H and the generalized polynomials, Int. Math. Forum, Vol. 6, 2011, pp. 529-539.
    12. P.Agarwal and S.Jain, Further Results on Fractional Calculus of Srivastava Polynomials, Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 2(2011), Pages 167-174.
    13. P.Agarwal and S.Jain,NEW FINITE DOUBLE INTEGRAL FORMULAE INVOLVING POLYNOMIALS AND FUNCTIONS OF GENERAL NATURE' Journal of Applied Mathematics, Statistics and Informatics; Volume 7, Number 2, 2011.
    14. P.Agarwal and S.Jain, On integrals involving product of H and the generalized polynomials, Acta Ciencia Indica, Vol. XXXVII M,No.1,167(2011), pp.167-174.
    15. P.Agarwal, S.Jain and M. Chand, Finite Integrals Involving Jacobi Polynomials and

    I-function, Theoretical Mathematics & Applications, vol.1, no.1, 2011, 115-123

    ISSN: 1792- 9687 (print), 1792-9709 (online).International Scientific Press, 2011.

    1. P.Agarwal and S.Jain, On multiple integral relations involving generalized Mellin-Barnes type of contour integral, To appear in TOJMS, (Taiwan).
    2. P.Agarwal, Fractional integration of the product of two H-functions and a general class of polynomials, To appear in Asian Journal of Applied Sciences,(USA).

    18.  P.Agarwal, Functional Relations Involving Generalized Mellin-Barnes Type of Contour Integral, To communicated for publication in Asian-European Journal of Mathematics.

    19.  P.Agarwal and S.Jain, Certain multiple integral relations involving generalized Mellin-Barnes type of contour integral, To communicated for publication ACTA UNIVERSITATIS APULENSIS.

     

    20.  P.Agarwal, S.Jain and M. Chand, New Bilateral Generating Functions Pertaining To I-function, To communicated for publication in Tamkang Journal of Mathematics.

    21.  P.Agarwal and S.Jain,  Integrals involving product of H, and, To Communicated for publication in Vijnana Parishad.

    22.  P.Agarwal, S.Jain and M. Chand ,Certain Integral Properties of Generalized Class of Polynomials and Generalized Contour Integral Associated with Feynman Integrals, To Communicated for publication in Journal of Applied Mathematics, Statistics and Informatics.

    23.  P.Agarwal, S.Jain and M. Chand, New Integral Formulas Involving Polynomials and -function, To communicate for publication in Journal of Applied Mathematics, Statistics and Informatics.

    24.  P.Agarwal, ON NEW APPLICATIONS OF FRACTIONAL CALCULUS, To communicate for publication in Journal of Inequalities and Special Functions.

    25.  P.Agarwal and Shilpi Jain, Bianchi Type-I Magnetized Cosmological Model in General Relativity , To communicate for publication in Journal of Jordan Journal of Math. & Stat.

    26.  P.Agarwal, ON APPLICATIONS OF FRACTIONAL CALCULUS INVOLVING SUMMATIONS OF SERIES, To communicate for publication in Journal of FCAA.

    27.  P.Agarwal, On a Unified Integral Involving the Product of Srivastava’s Polynomials and Generalized Mellin-Barnes Type Contour Integral, To communicate for publication in Journal of Bulletin of Mathematical Analysis and Applications.

    BOOK PUBLICATIONS

     

    Published

    1. Engineering Mathematics-I

    Published in Paragon International Publishers, New Delhi, 2007.

    1. Advanced Mathematics (EC, EIC, EE)

    Published in Paragon International Publishers, New Delhi, 2008.

    1. Advanced Engineering Mathematics-IV

    Published in Nandani Prakashan Pvt. Ltd., 2011.

    1. Engineering Mathematics-III (Computer science Engg.)

    Under the Publication in Nandani Prakashan Pvt. Ltd., 2012.

    1. Engineering Mathematics-II

    Under the Paragon International Publishers, New Delhi, 2012.

     

     

     

     

     

     

    REFERENCES

    1.      Prof. Kantesh Gupta, Professor in Department of Mathematics, Malviya National Institute of Technology, Jaipur, Inida,e-mail : Update_this_ID115@mnit.ac.in (Tel.)0141-2713257.
    1. Prof. K. C. Gupta, Emeritus Fellow, AICTE, A-II, 106 Nagar Residency, Mahavir Nager, Jaipur, Inida,e-mail : kcgupta_ in2000@yahoo.com (Tel.)0141-2701339.
    2. Prof. M. A. Pathan, Department of Mathematics, Aligarh Muslim University, Aligarh, India.
    1. Prof. Remy Y. Denis, Department of Mathematics, Gorakhpur University, Gorakhpur - 273009, India, e-mail: ddry@sancharnet.in , ddry@rediffmail.com ; Tel # 91 551 2500750

     

     

    Yours sincerely

     

    Dr Praveen Agarwal

    Associate Professor of Mathematics & Head of Department

    Anand International College of Engineering, Jaipur

    Agara Road, Near Kanota.

    INDIA-302012.

     

     

     

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Published

2012-11-07

Issue

Vol. 67 No. 2 (2012)

Section

Articoli

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