Opial type inequalities for conformable fractional derivative and integral of two functions
Keywords:
Opial type inequality; Conformable fractional derivative; Conformable fractional integral.
Abstract
In this paper, we establish the Opial type inequalities for conformable fractional derivative and integral of two function and give some results in special cases of alpha.
Downloads
Download data is not yet available.
References
[1] Agarwal, RP, Pang, PYH (1995). Opial Inequalities with Apphications in Differential and Difference
Equations. Kluwer Academic Publlshers.
[2] Cheung, WS, Dandan, Z, Pečarić, J (2007). Opial-type inequalities for differential operators. Nonlinear
Analysis Theory Methods & Applications, 66(9), 2028-2039.
[3] Andrić, M, Barbir, A, Farid, G, Pečarić, J (2014). Opial-type inequality due to Agarwal-Pang and fractional
differential inequalities. Integral Transforms & Special Function, 25(4), 324-335.
[4] Iqbal, S, Pečarić, J, Samraiz, M (2015). Multiple Opial-Type Inequalities for General Kernels with
Applications. Journal of Mathematical Inequalities, 9(2), 381-396.
[5] Hsu, KC, Tseng, KL (2015). Some New Discrete Inequalities of Opial and Lasota's Type. Journal of
Progressive Research in Mathematics, 4(2), 294-302.
[6] Li, LZ, Han, MA (2014). Some new dynamic Opial type inequalities and applications for second order integrodifferential dynamic equations on time scales. Applied Mathematics & Computation, 232(6), 542-547.
[7] Rabie, SS, Saker, SH, Agarwal, RP (2016). Opial type inequalities with two unknowns and two functions on
time scales. Vietnam Journal of Mathematics, 44(3), 541-555.
[8] Andrić, M, Pečarić, J, Perić, I (2013). An Opial-Type inequality for fractional derivatives of two functions.
Fractional Differential Calculus, 3(1), 55-68.
[9] Sarikaya, MZ, Budak, H (2016). Opial Type inequalities for conformable fractional integrals.
https://www.researchgate.net/publication/303487107.
[10] Iqbal, S, Pečarić, J, Samraiz, M (2014). Opial-Type inequalities for two functions with general kernels and
applications. Journal of Mathematical Inequalities, 8(4), 757-775.
[11] Abdeljawad, T (2015). On conformable fractional calculus. Journal of Computational and Applied
Mathematics, 279, 57-66.
[12] Hammad, MA, Khalil, R (2014). Conformable fractional heat differential equations. International Journal of
Differential Equations and Applications, 13(3), 177-183.
[13] Iyiola, OS, Nwaeze, ER (2016). Some new results on the new conformable fractional calculus with application
using D'Alambert approach. Progress in Fractional Differentiation and Applications, 2(2), 115-121.
Equations. Kluwer Academic Publlshers.
[2] Cheung, WS, Dandan, Z, Pečarić, J (2007). Opial-type inequalities for differential operators. Nonlinear
Analysis Theory Methods & Applications, 66(9), 2028-2039.
[3] Andrić, M, Barbir, A, Farid, G, Pečarić, J (2014). Opial-type inequality due to Agarwal-Pang and fractional
differential inequalities. Integral Transforms & Special Function, 25(4), 324-335.
[4] Iqbal, S, Pečarić, J, Samraiz, M (2015). Multiple Opial-Type Inequalities for General Kernels with
Applications. Journal of Mathematical Inequalities, 9(2), 381-396.
[5] Hsu, KC, Tseng, KL (2015). Some New Discrete Inequalities of Opial and Lasota's Type. Journal of
Progressive Research in Mathematics, 4(2), 294-302.
[6] Li, LZ, Han, MA (2014). Some new dynamic Opial type inequalities and applications for second order integrodifferential dynamic equations on time scales. Applied Mathematics & Computation, 232(6), 542-547.
[7] Rabie, SS, Saker, SH, Agarwal, RP (2016). Opial type inequalities with two unknowns and two functions on
time scales. Vietnam Journal of Mathematics, 44(3), 541-555.
[8] Andrić, M, Pečarić, J, Perić, I (2013). An Opial-Type inequality for fractional derivatives of two functions.
Fractional Differential Calculus, 3(1), 55-68.
[9] Sarikaya, MZ, Budak, H (2016). Opial Type inequalities for conformable fractional integrals.
https://www.researchgate.net/publication/303487107.
[10] Iqbal, S, Pečarić, J, Samraiz, M (2014). Opial-Type inequalities for two functions with general kernels and
applications. Journal of Mathematical Inequalities, 8(4), 757-775.
[11] Abdeljawad, T (2015). On conformable fractional calculus. Journal of Computational and Applied
Mathematics, 279, 57-66.
[12] Hammad, MA, Khalil, R (2014). Conformable fractional heat differential equations. International Journal of
Differential Equations and Applications, 13(3), 177-183.
[13] Iyiola, OS, Nwaeze, ER (2016). Some new results on the new conformable fractional calculus with application
using D'Alambert approach. Progress in Fractional Differentiation and Applications, 2(2), 115-121.
Published
2017-09-07
How to Cite
Han, X., Li, S., & Li, Q. (2017). Opial type inequalities for conformable fractional derivative and integral of two functions. Journal of Progressive Research in Mathematics, 12(3), 1924-1931. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1222
Issue
Section
Articles
Copyright (c) 2017 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.