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The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators

Yıl 2023, Cilt: 6 Sayı: 3, 135 - 141, 17.09.2023

Kalpana Rajput Rajshree Mıshra Deepak Kumar Jain Altaf Ahmad Bhat , Farooq Ahmad

https://doi.org/10.33434/cams.1275523

Öz

This work uses the Marichev-Saigo-Maeda (MSM) fractional integral operator to achieve certain special fractional integral inequalities for synchronous functions. Compared to the previously mentioned classical inequalities, the inequalities reported in this study are more widespread. We also looked at several unique instances of these inequalities involving the fractional operators of the Saigo, Erdelyi, and Kober, and Riemann-Liouville types.

Anahtar Kelimeler

Fractional Integral Inequalities Saigo–Maeda Operators Synchronous functions

Kaynakça

  • [1] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, (1993).
  • [2] V. Kiryakova, Generalized Fractional Calculus and Applications, Wiley, New York, (1994).
  • [3] J.L. Lavoie, T.J. Osler, R. Tremblay, Fractional derivatives and special functions, 18(2) (1976), 240-268.
  • [4] V. Kiryakova, All the special functions are fractional differ integrals of elementary functions, J. Physics A: Math. and Gen., 30 (1997), 5085-5103.
  • [5] V. Kiryakova, The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus, Computers and Mathematics with Applications, 59(5) (2010), 1885-1895.
  • [6] M. Ciesielskia, M. Klimekb, T. Blaszczykb, The Fractional Sturm-Liouville Problem - Numerical Approximation and Application in Fractional Diffusion, J. Comput. Appl. Math., 317 (2017), 573-588.
  • [7] V. Kiryakova, Fractional calculus operators of special functions? The result is well predictable, Chaos Solitons Fractals, 102 (2017), 1-14.
  • [8] M. Saigo, R.K. Saxena, J. Ram, On the fractional calculus operator associated with the H- function, Gonita Sandesh, 6(1) (1992).
  • [9] S. Jahanshahi, E. Babolian, D.F.M. Torres, A.R. Vahidi, A fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives, Chaos Solitons Fractals, 102 (2017), 295-304.
  • [10] D. Baleanu, A. Fernandez, On fractional operators and their classifications, Mathematics, 7(9) (2019), 830.
  • [11] A. Ekinci, M. Ozdemir, Some new integral inequalities via Riemann Liouville integral operators,Appl. Comput. Math., 18(3) (2019), 288-295.
  • [12] S.I. Butt, M. Nadeem, G. Farid, On Caputo fractional derivatives via exponential s-convex functions, Turkish J. Sci., 5(2) (2020), 140-146.
  • [13] S. Kizil, M.A. Ardi, Inequalities for strongly convex functions via Atangana Baleanu integral operators, Turkish J. Sci., 6(2) (2021), 96-109.
  • [14] H. Kalsoom, M.A. Ali, M. Abbas, H. Budak, G. Murtaza, Generalized quantum Montgomery identity and Ostrowski type inequalities for preinvex functions, TWMS J. Pure Appl. Math., 13(1) (2022), 72-90.
  • [15] J.A. Canavati, The Riemann-Liouville integral, Nieuw Archief Voor Wiskunde, 5(1) (1987), 53-75.
  • [16] S.D. Purohit, R.K. Raina, Chebyshev type inequalities for the Saigo fractional integral and their q-analogues, J. Math. Inequal., 7(2) (2013), 239–249.
  • [17] L. Curiel, L. Galue, A generalization of the integral operators involving the Gauss hypergeometric function, Revista Tecnica de la Facultad de Ingenierıa Universidad del Zulia, 19(1) (1996), 17–22.
  • [18] Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci., 9(4) (2010), 493–497.
  • [19] T.J. Olser, Leibniz rule for Fractional Derivatives Generalized and an Application to Infinite Series, SIAM. J. Appl. Math., 18 (1970), 658-678.
  • [20] R. Herrmann, Towards a geometric interpretation of generalized fractional integrals-Erdelyi-Kober type integrals on R N, as an example, Fract. Calc. Appl. Anal., 17(2) (2014), 361-370.
  • [21] S.S. Zhou, S. Rashid, S. Parveen, A.O. Akdemir, Z. Hammouch, New computations for extended weighted functionals within the Hilfer generalized proportional fractional integral operators, AIMS Math, 6(5) (2021), 4507-4525.
  • [22] M. Saigo, A Remark on Integral Operators involving the Gauss hypergeometric functions, Math. Rep. College General Ed.Kyushu Univ., 11 (1978), 135-143.
  • [23] M. Saigo, A certain boundary value problem for the Euler-Darboux equation, Math. Japonica, 24(4) (1979), 377-385.
  • [24] S. Jain, R. Goyal, P. Agarwal, S. Momani, Certain Saigo type fractional integral inequalities and their q-analogues, An International Journal of Optimization and Control: Theories and Applications (IJOCTA), 13(1) (2023), 1-9.

Yıl 2023, Cilt: 6 Sayı: 3, 135 - 141, 17.09.2023

Kalpana Rajput Rajshree Mıshra Deepak Kumar Jain Altaf Ahmad Bhat , Farooq Ahmad

https://doi.org/10.33434/cams.1275523

Öz

Kaynakça

  • [1] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, (1993).
  • [2] V. Kiryakova, Generalized Fractional Calculus and Applications, Wiley, New York, (1994).
  • [3] J.L. Lavoie, T.J. Osler, R. Tremblay, Fractional derivatives and special functions, 18(2) (1976), 240-268.
  • [4] V. Kiryakova, All the special functions are fractional differ integrals of elementary functions, J. Physics A: Math. and Gen., 30 (1997), 5085-5103.
  • [5] V. Kiryakova, The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus, Computers and Mathematics with Applications, 59(5) (2010), 1885-1895.
  • [6] M. Ciesielskia, M. Klimekb, T. Blaszczykb, The Fractional Sturm-Liouville Problem - Numerical Approximation and Application in Fractional Diffusion, J. Comput. Appl. Math., 317 (2017), 573-588.
  • [7] V. Kiryakova, Fractional calculus operators of special functions? The result is well predictable, Chaos Solitons Fractals, 102 (2017), 1-14.
  • [8] M. Saigo, R.K. Saxena, J. Ram, On the fractional calculus operator associated with the H- function, Gonita Sandesh, 6(1) (1992).
  • [9] S. Jahanshahi, E. Babolian, D.F.M. Torres, A.R. Vahidi, A fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives, Chaos Solitons Fractals, 102 (2017), 295-304.
  • [10] D. Baleanu, A. Fernandez, On fractional operators and their classifications, Mathematics, 7(9) (2019), 830.
  • [11] A. Ekinci, M. Ozdemir, Some new integral inequalities via Riemann Liouville integral operators,Appl. Comput. Math., 18(3) (2019), 288-295.
  • [12] S.I. Butt, M. Nadeem, G. Farid, On Caputo fractional derivatives via exponential s-convex functions, Turkish J. Sci., 5(2) (2020), 140-146.
  • [13] S. Kizil, M.A. Ardi, Inequalities for strongly convex functions via Atangana Baleanu integral operators, Turkish J. Sci., 6(2) (2021), 96-109.
  • [14] H. Kalsoom, M.A. Ali, M. Abbas, H. Budak, G. Murtaza, Generalized quantum Montgomery identity and Ostrowski type inequalities for preinvex functions, TWMS J. Pure Appl. Math., 13(1) (2022), 72-90.
  • [15] J.A. Canavati, The Riemann-Liouville integral, Nieuw Archief Voor Wiskunde, 5(1) (1987), 53-75.
  • [16] S.D. Purohit, R.K. Raina, Chebyshev type inequalities for the Saigo fractional integral and their q-analogues, J. Math. Inequal., 7(2) (2013), 239–249.
  • [17] L. Curiel, L. Galue, A generalization of the integral operators involving the Gauss hypergeometric function, Revista Tecnica de la Facultad de Ingenierıa Universidad del Zulia, 19(1) (1996), 17–22.
  • [18] Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci., 9(4) (2010), 493–497.
  • [19] T.J. Olser, Leibniz rule for Fractional Derivatives Generalized and an Application to Infinite Series, SIAM. J. Appl. Math., 18 (1970), 658-678.
  • [20] R. Herrmann, Towards a geometric interpretation of generalized fractional integrals-Erdelyi-Kober type integrals on R N, as an example, Fract. Calc. Appl. Anal., 17(2) (2014), 361-370.
  • [21] S.S. Zhou, S. Rashid, S. Parveen, A.O. Akdemir, Z. Hammouch, New computations for extended weighted functionals within the Hilfer generalized proportional fractional integral operators, AIMS Math, 6(5) (2021), 4507-4525.
  • [22] M. Saigo, A Remark on Integral Operators involving the Gauss hypergeometric functions, Math. Rep. College General Ed.Kyushu Univ., 11 (1978), 135-143.
  • [23] M. Saigo, A certain boundary value problem for the Euler-Darboux equation, Math. Japonica, 24(4) (1979), 377-385.
  • [24] S. Jain, R. Goyal, P. Agarwal, S. Momani, Certain Saigo type fractional integral inequalities and their q-analogues, An International Journal of Optimization and Control: Theories and Applications (IJOCTA), 13(1) (2023), 1-9.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Kalpana Rajput 0009-0003-7687-8581

Rajshree Mıshra 0000-0003-1331-0908

Deepak Kumar Jain 0000-0002-4252-6719

Altaf Ahmad Bhat 0000-0001-7605-9971

Farooq Ahmad 0009-0007-4184-9042

Erken Görünüm Tarihi 12 Eylül 2023
Yayımlanma Tarihi 17 Eylül 2023
Gönderilme Tarihi 2 Nisan 2023
Kabul Tarihi 4 Eylül 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 3

Kaynak Göster

APA Rajput, K., Mıshra, R., Jain, D. K., Bhat, A. A., vd. (2023). The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators. Communications in Advanced Mathematical Sciences, 6(3), 135-141. https://doi.org/10.33434/cams.1275523
AMA Rajput K, Mıshra R, Jain DK, Bhat AA, Ahmad F. The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators. Communications in Advanced Mathematical Sciences. Eylül 2023;6(3):135-141. doi:10.33434/cams.1275523
Chicago Rajput, Kalpana, Rajshree Mıshra, Deepak Kumar Jain, Altaf Ahmad Bhat, ve Farooq Ahmad. “The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators”. Communications in Advanced Mathematical Sciences 6, sy. 3 (Eylül 2023): 135-41. https://doi.org/10.33434/cams.1275523.
EndNote Rajput K, Mıshra R, Jain DK, Bhat AA, Ahmad F (01 Eylül 2023) The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators. Communications in Advanced Mathematical Sciences 6 3 135–141.
IEEE K. Rajput, R. Mıshra, D. K. Jain, A. A. Bhat, ve F. Ahmad, “The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators”, Communications in Advanced Mathematical Sciences, c. 6, sy. 3, ss. 135–141, 2023, doi: 10.33434/cams.1275523.
ISNAD Rajput, Kalpana vd. “The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators”. Communications in Advanced Mathematical Sciences 6/3 (Eylül 2023), 135-141. https://doi.org/10.33434/cams.1275523.
JAMA Rajput K, Mıshra R, Jain DK, Bhat AA, Ahmad F. The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators. Communications in Advanced Mathematical Sciences. 2023;6:135–141.
MLA Rajput, Kalpana vd. “The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators”. Communications in Advanced Mathematical Sciences, c. 6, sy. 3, 2023, ss. 135-41, doi:10.33434/cams.1275523.
Vancouver Rajput K, Mıshra R, Jain DK, Bhat AA, Ahmad F. The Fractional Integral Inequalities Involving Kober and Saigo–Maeda Operators. Communications in Advanced Mathematical Sciences. 2023;6(3):135-41.
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