New estimates considering the generalized proportional Hadamard fractional integral operators
In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integr...
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| Vydané v: | Advances in difference equations Ročník 2020; číslo 1; s. 1 - 15 |
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| Jazyk: | English |
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Springer International Publishing
09.06.2020
Springer Nature B.V SpringerOpen |
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| ISSN: | 1687-1847, 1687-1839, 1687-1847 |
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| Abstract | In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators. |
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| AbstractList | In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators. Abstract In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators. |
| ArticleNumber | 275 |
| Author | Rashid, Saima Chu, Yu-Ming Jarad, Fahd Zhou, Shuang-Shuang Kalsoom, Humaira |
| Author_xml | – sequence: 1 givenname: Shuang-Shuang surname: Zhou fullname: Zhou, Shuang-Shuang organization: School of Science, Hunan City University – sequence: 2 givenname: Saima surname: Rashid fullname: Rashid, Saima organization: Department of mathematics, Government University – sequence: 3 givenname: Fahd surname: Jarad fullname: Jarad, Fahd organization: Department of Mathematics, Çankaya University – sequence: 4 givenname: Humaira surname: Kalsoom fullname: Kalsoom, Humaira organization: School of Mathematical Sciences, Zhejiang University – sequence: 5 givenname: Yu-Ming surname: Chu fullname: Chu, Yu-Ming email: chuyuming2005@126.com organization: Department of Mathematics, Huzhou University, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology |
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| Keywords | 26E60 Grüss inequality Generalized proportional Hadamard fractional integral operator 26D10 Riemann–Liouville fractional integral operator 90C23 Fractional calculus 26D15 |
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| References | Rashid, Jarad, Chu (CR19) 2020; 2020 Zhou, Huang, Hu, Liu (CR22) 2013; 2013 Kiryakova (CR33) 1994 Dahmani (CR44) 2010; 9 Zhao, Shi, Chu (CR56) 2020; 114 Rashid, Noor, Noor, Chu (CR53) 2020; 5 Abdeljawad, Baleanu (CR2) 2017; 2017 Zhou (CR14) 2015; 9 Wang, Hong, Xu, Shen, Chu (CR59) 2020; 14 Ghanbari, Kumar, Kumar (CR5) 2020; 133 Kreyszig (CR38) 1989 Awan, Talib, Chu, Noor, Noor (CR29) 2020; 2020 Rashid, Jarad, Noor, Kalsoom, Chu (CR18) 2019; 7 Iqbal, Adil Khan, Ullah, Chu (CR27) 2020; 2020 Baleanu, Diethelm, Scalas, Trujillo (CR34) 2012 Jarad, Uğurlu, Abdeljawad, Baleanu (CR35) 2017; 2017 CR6 Kilbas, Srivastava, Trujillo (CR37) 2006 Abdeljawad (CR1) 2015; 279 CR9 Kumar, Nisar, Kumar, Cattani, Samet (CR10) 2020; 43 Pratap, Raja, Cao, Alzabut, Huang (CR26) 2020; 2020 Zhou, Jiang (CR25) 2019; 42 Jarad, Abdeljawad, Alzabut (CR41) 2017; 226 Wu (CR12) 2014; 2014 Kumar, Kumar, Abbas, Al Qurashi, Baleanu (CR7) 2020; 2020 Sharma, Kumar, Cattani, Baleanu (CR39) 2020; 15 Yang, Qian, Zhang, Chu (CR58) 2020; 23 Alzabut, Abdeljawad, Jarad, Sudsutad (CR3) 2019; 2019 Huang, Liu (CR15) 2017; 40 Wu, Liu (CR21) 2013; 42 Samko, Kilbas, Marichev (CR42) 1993 Rafeeq, Kalsoom, Hussain, Rashid, Chu (CR50) 2020; 2020 Zhao, Chu, Wang (CR54) 2011; 2011 Miller, Ross (CR31) 1993 Grüss (CR47) 1935; 39 Dahmani, Tabharit, Taf (CR45) 2010; 2 Rashid, Ashraf, Noor, Noor, Chu (CR51) 2020; 5 Mathai (CR32) 2005; 396 Doungmo, Emile, Kumar, Mugisha (CR4) 2020; 130 Kumar, Kumar, Agarwal, Samet (CR8) 2020; 2020 Rashid, Jarad, Kalsoom, Chu (CR28) 2020; 2020 Rashid, Noor, Noor, Safdar, Chu (CR52) 2019; 7 Wang, Chu, Li, Chu (CR60) 2020; 14 Sudsutad, Ntouyas, Tariboon (CR48) 2014; 2014 Sharma, Kumar, Paswan (CR40) 2018; 36 Zaheer Ullah, Adil Khan, Chu (CR57) 2019; 2019 Liu, Feng, Anh, Li (CR23) 2019; 78 Huang, Liu (CR20) 2012; 92 Huang, Guo, Liu (CR13) 2014; 8 Tan, Liu (CR16) 2017; 111 Khalil, Al Horani, Yousef, Sababheh (CR36) 2014; 264 Denton, Vatsala (CR46) 2010; 59 Yang, Qian, Chu, Zhang (CR55) 2017; 2017 Jiang, Xu (CR24) 2019; 62 Hu, Liu (CR17) 2017; 101 Rahman, Khan, Abdeljawad, Nisar (CR43) 2019; 2019 Rahman, Abdeljawad, Jarad, Khan, Nisar (CR49) 2019; 2019 Wu, Liu (CR11) 2013; 2013 Chu, Adil Khan, Ali, Dragomir (CR30) 2017; 2017 G. Rahman (2730_CR43) 2019; 2019 J. Alzabut (2730_CR3) 2019; 2019 V. Kiryakova (2730_CR33) 1994 2730_CR6 B. Sharma (2730_CR39) 2020; 15 2730_CR9 A. Iqbal (2730_CR27) 2020; 2020 C.-X. Huang (2730_CR15) 2017; 40 S.G. Samko (2730_CR42) 1993 D. Baleanu (2730_CR34) 2012 S. Rashid (2730_CR53) 2020; 5 S.-H. Zhou (2730_CR25) 2019; 42 S. Rashid (2730_CR51) 2020; 5 S. Rashid (2730_CR19) 2020; 2020 J. Wu (2730_CR12) 2014; 2014 F. Jarad (2730_CR35) 2017; 2017 G. Doungmo (2730_CR4) 2020; 130 S. Kumar (2730_CR10) 2020; 43 B. Sharma (2730_CR40) 2018; 36 E. Kreyszig (2730_CR38) 1989 J. Wu (2730_CR11) 2013; 2013 T. Abdeljawad (2730_CR2) 2017; 2017 G. Rahman (2730_CR49) 2019; 2019 S. Kumar (2730_CR8) 2020; 2020 S. Kumar (2730_CR7) 2020; 2020 B. Ghanbari (2730_CR5) 2020; 133 X.-S. Zhou (2730_CR14) 2015; 9 C.-X. Huang (2730_CR13) 2014; 8 S. Rafeeq (2730_CR50) 2020; 2020 M.-K. Wang (2730_CR59) 2020; 14 Z.-H. Yang (2730_CR55) 2017; 2017 Z. Denton (2730_CR46) 2010; 59 Y.-M. Chu (2730_CR30) 2017; 2017 R. Khalil (2730_CR36) 2014; 264 A.A. Kilbas (2730_CR37) 2006 W. Sudsutad (2730_CR48) 2014; 2014 Z. Dahmani (2730_CR45) 2010; 2 S. Rashid (2730_CR18) 2019; 7 M.U. Awan (2730_CR29) 2020; 2020 T.-H. Zhao (2730_CR54) 2011; 2011 Z.-H. Yang (2730_CR58) 2020; 23 H.-J. Hu (2730_CR17) 2017; 101 T.-H. Zhao (2730_CR56) 2020; 114 S. Rashid (2730_CR28) 2020; 2020 C.-X. Huang (2730_CR20) 2012; 92 A.M. Mathai (2730_CR32) 2005; 396 T. Abdeljawad (2730_CR1) 2015; 279 F. Jarad (2730_CR41) 2017; 226 S. Rashid (2730_CR52) 2019; 7 A. Pratap (2730_CR26) 2020; 2020 K.S. Miller (2730_CR31) 1993 F.-W. Liu (2730_CR23) 2019; 78 J. Wu (2730_CR21) 2013; 42 Y.-X. Tan (2730_CR16) 2017; 111 Z. Dahmani (2730_CR44) 2010; 9 X.-S. Zhou (2730_CR22) 2013; 2013 Y.-J. Jiang (2730_CR24) 2019; 62 G. Grüss (2730_CR47) 1935; 39 S. Zaheer Ullah (2730_CR57) 2019; 2019 M.-K. Wang (2730_CR60) 2020; 14 |
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| SubjectTerms | Analysis Applications Difference and Functional Equations Fractional calculus Functional Analysis Generalized proportional Hadamard fractional integral operator Grüss inequality Integrals Mathematics Mathematics and Statistics Methods Operators (mathematics) Ordinary Differential Equations Partial Differential Equations Riemann–Liouville fractional integral operator Topics in Special Functions and q-Special Functions: Theory |
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| Title | New estimates considering the generalized proportional Hadamard fractional integral operators |
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