Ψ- RIMAN-LIUVILL KASR INTEGRALLARI UCHUN HARDI-LITTLEVUD TENGSIZLIGI HAQIDAGI TEOREMALAR.
Keywords:
Hardi va Littlevud tengsizligi, Riman-Liuvill integrali, ψ-Riman-Liuvill kasr integrali, Gyolder tengsizligi, musbat o‘suvchi funksiya.Abstract
Lebeg fazosida -Riman-Liuvill tipidagi kasrli integralning chegaralanganligi va Hardi-Littlevud tengsizligi haqidagi teoremalari isbotlangan
References
Ahmad B., Alsaed A., Ntouyas S. K. and J. Tariboon,Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities, Springer, Berlin, 2017, — 414 pages.
Butzer P.L., Kilbas A.A. and Trujillo J.J. Fractional calculus in the Mellin setting and Hadamard-type fractional integrals // Journal of Mathematical Analysis and Applications. — 2002. —Vol 269, № 1. — P. 1-27.
Butzer P.L., Kilbas A.A. and Trujillo J.J. Compositions of Hadamard-type
fractional integration operators and the semigroup property. Journal of
Mathematical Analysis and Applications. — 2002. Vol. 269, № 2. —P. 387-400.
Butzer P.L., Kilbas A.A.and Trujillo J.J. Mellin transform analysis and integration by parts for Hadamard-type fractional integrals // Journal of Mathematical Analysis and Applications. — 2002. — Vol. 270,.№ 1. — P. 1-15.
Hadamard J. Essai sur l‘etude des functions donn´ees par leur d´eveloppment de Taylor// J. Math. Pures et Appl.. —1892. —Vol. 8, Ser. 4. —P. 101-186.
Hilfer R. Applications of Fractional Calculus in Physics // Singapore: World Scientific, 2000.—204 p.
Kilbas A. A. Hadamard-type fractional calculus // J. Korean Math. Soc..—2001.—Vol. 38, Issue 6.—P. 1191–1204.