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Volumn 81, Issue 2-3, 1997, Pages 287-304

Fractional calculus operators and their applications involving power functions and summation of series

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EID: 0007160709     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(95)00310-X     Document Type: Article
Times cited : (12)

References (31)
  • 1
    • 0003654359 scopus 로고
    • Pitman Research Notes in Mathematics Series 301, Longman Scientific and Technical, Harlow, Essex (John Wiley and Sons, New York)
    • V. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Research Notes in Mathematics Series 301, Longman Scientific and Technical, Harlow, Essex (John Wiley and Sons, New York), 1994.
    • (1994) Generalized Fractional Calculus and Applications
    • Kiryakova, V.1
  • 3
    • 23644446042 scopus 로고
    • Descartes Press, Koriyama
    • K. Nishimoto, Fractional Calculus, Vols. I, II, III, and IV, Descartes Press, Koriyama, 1984, 1987, 1989, and 1991.
    • (1984) Fractional Calculus , vol.1-4
    • Nishimoto, K.1
  • 8
    • 0003521743 scopus 로고
    • Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto
    • H. M. Srivastava and S. Owa (Eds.), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1989.
    • (1989) Univalent Functions, Fractional Calculus, and Their Applications
    • Srivastava, H.M.1    Owa, S.2
  • 9
    • 0006972557 scopus 로고
    • Functions that have no first-order derivative might have fractional derivatives of all orders less than 1
    • B. Ross, S. G. Samko, and E. R. Love, Functions That Have no First-Order Derivative Might Have Fractional Derivatives of All Orders Less Than 1, Real Anal. Exchange 20:140-157 (1994/1995).
    • (1994) Real Anal. Exchange , vol.20 , pp. 140-157
    • Ross, B.1    Samko, S.G.2    Love, E.R.3
  • 11
    • 23644454521 scopus 로고
    • Power Functions in fractional calculus of nishimoto and that of lacroix and riemann-Liouville
    • K. Nishimoto, Power Functions in Fractional Calculus of Nishimoto and That of Lacroix and Riemann-Liouville, J. Fractional Calculus 2:11-25 (1992).
    • (1992) J. Fractional Calculus , vol.2 , pp. 11-25
    • Nishimoto, K.1
  • 13
    • 0040829134 scopus 로고
    • A Note on a certain fractional integral formula
    • H. M. Srivastava and K. Nishimoto, A Note on a Certain Fractional Integral Formula, J. Fractional Calculus 3:87-89 (1993).
    • (1993) J. Fractional Calculus , vol.3 , pp. 87-89
    • Srivastava, H.M.1    Nishimoto, K.2
  • 16
    • 38249026911 scopus 로고
    • A class of distortion theorems involving certain operators of fractional calculus
    • H. M. Srivastava, M. Saigo, and S. Owa, A Class of Distortion Theorems Involving Certain Operators of Fractional Calculus, J. Math. Anal. Appl. 131:412-420 (1988).
    • (1988) J. Math. Anal. Appl. , vol.131 , pp. 412-420
    • Srivastava, H.M.1    Saigo, M.2    Owa, S.3
  • 17
    • 0001786148 scopus 로고
    • Certain classes of infinite series summable by means of fractional calculus
    • K. Nishimoto and H. M. Srivastava, Certain Classes of Infinite Series Summable by Means of Fractional Calculus, J. College Engrg. Nihon Univ. Ser. B 30:97-106 (1989).
    • (1989) J. College Engrg. Nihon Univ. Ser. B , vol.30 , pp. 97-106
    • Nishimoto, K.1    Srivastava, H.M.2
  • 18
    • 0002854846 scopus 로고
    • A simple algorithm for the evaluation of a class of generalized hypergeometric series
    • H. M. Srivastava, A Simple Algorithm for the Evaluation of a Class of Generalized Hypergeometric Series, Stud. Appl Math. 86:79-86 (1992).
    • (1992) Stud. Appl Math. , vol.86 , pp. 79-86
    • Srivastava, H.M.1
  • 19
    • 0001411037 scopus 로고
    • A certain family of infinite series associated with digamma functions
    • B. N. Al-Saqabi, S. L. Kalla, and H. M. Srivastava, A Certain Family of Infinite Series Associated with Digamma Functions, J. Math. Anal. Appl. 159:361-372 (1991).
    • (1991) J. Math. Anal. Appl. , vol.159 , pp. 361-372
    • Al-Saqabi, B.N.1    Kalla, S.L.2    Srivastava, H.M.3
  • 20
    • 0001766241 scopus 로고
    • Fractional calculus and the sums of certain families of infinite series
    • J. Aular de Durán, S. L. Kalla, and H. M. Srivastava, Fractional Calculus and the Sums of Certain Families of Infinite Series, J. Math. Anal. Appl. 190:738-754 (1995).
    • (1995) J. Math. Anal. Appl. , vol.190 , pp. 738-754
    • Aular De Durán, J.1    Kalla, S.L.2    Srivastava, H.M.3
  • 21
    • 23644446691 scopus 로고
    • A certain family of infinite series, differintegrable functions and psi functions
    • S.-T. Tu and D.-K. Chyan, A Certain Family of Infinite Series, Differintegrable Functions and Psi Functions, J. Fractional Calculus 7:41-46 (1995);
    • (1995) J. Fractional Calculus , vol.7 , pp. 41-46
    • Tu, S.-T.1    Chyan, D.-K.2
  • 23
  • 24
    • 0347845966 scopus 로고
    • Application of fractional calculus to infinite sums (II)
    • L. Galué, Application of Fractional Calculus to Infinite Sums (II), J. Fractional Calculus 7:61-67 (1995).
    • (1995) J. Fractional Calculus , vol.7 , pp. 61-67
    • Galué, L.1
  • 25
    • 0006988345 scopus 로고
    • Notes on the generalized derivative of riemann-liouville and Its applications to leibniz's formula. I and II
    • Y. Watanabe, Notes on the Generalized Derivative of Riemann-Liouville and Its Applications to Leibniz's Formula. I and II, Tôhoku Math. J. 34:8-27 and 28-41 (1931).
    • (1931) Tôhoku Math. J. , vol.34
    • Watanabe, Y.1
  • 26
    • 0014782163 scopus 로고
    • Leibniz rule for fractional derivatives generalized and an application to infinite series
    • T. J. Osler, Leibniz Rule for Fractional Derivatives Generalized and an Application to Infinite Series, SIAM J. Appl. Math. 18:658-674 (1970).
    • (1970) SIAM J. Appl. Math. , vol.18 , pp. 658-674
    • Osler, T.J.1
  • 27
    • 0346585875 scopus 로고
    • An application of generalized leibniz rule to infinite sums
    • A. Al-Zamel and S. Kalla, An Application of Generalized Leibniz Rule to Infinite Sums, J. Fractional Calculus 7:29-33 (1995).
    • (1995) J. Fractional Calculus , vol.7 , pp. 29-33
    • Al-Zamel, A.1    Kalla, S.2
  • 28
    • 23644452545 scopus 로고
    • An application of the fractional derivative to hypergeometric series
    • S. Owa, An Application of the Fractional Derivative to Hypergeometric Series (in Japanese), Sugaku 38:360-362 (1986).
    • (1986) Sugaku , vol.38 , pp. 360-362
    • Owa, S.1
  • 30
    • 0007156355 scopus 로고
    • A useful hypergeometric transformation
    • R. K. Samtani and R. C. Bhatt, A Useful Hypergeometric Transformation, Ganita Sandesh 8:65-67 (1994).
    • (1994) Ganita Sandesh , vol.8 , pp. 65-67
    • Samtani, R.K.1    Bhatt, R.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.