المؤلفون: Sanjay Bhatter, Sunil Dutt Purohit, Kamlesh Jangid, Sapna Meena

المصدر: Journal of Fractional Calculus and Nonlinear Systems. 2:42-50

مصطلحات موضوعية: Pure mathematics, Leibniz integral rule, symbols.namesake, Overline, symbols, Type (model theory), Mathematics, Fractional calculus

الوصف: In this paper, we determine some expansion formulae of the incomplete I-functions in affiliation with the Leibniz rule for the Riemann-Liouville type derivatives. Further, expansion formulae of the incomplete $\overline{I}$-function, incomplete $\overline{H}$-function, and incomplete H-function are conferred as extraordinary instances of our primary outcomes.

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_________::05120d61b6a73d37846ddb8adf7ec535
https://doi.org/10.48185/jfcns.v2i1.231

المؤلفون: Kamlesh Jangid, Sanjay Bhatter, Dumitru Baleanu, Maysaa Mohamed Al Qurashi, Sapna Meena, Sunil Dutt Purohit

المصدر: Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-24 (2020)

مصطلحات موضوعية: Algebra and Number Theory, Partial differential equation, 020209 energy, Applied Mathematics, lcsh:Mathematics, Incomplete gamma functions, 02 engineering and technology, Incomplete I-functions, Mellin–Barnes type contour, lcsh:QA1-939, 01 natural sciences, Fractional calculus, 010101 applied mathematics, Ordinary differential equation, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, 0101 mathematics, Fractional calculus operators, Analysis, Mathematics

الوصف: In this article, several interesting properties of the incomplete I-functions associated with the Marichev–Saigo–Maeda (MSM) fractional operators are studied and investigated. It is presented that the order of the incomplete I-functions increases about the utilization of the above-mentioned operators toward the power multiple of the incomplete I-functions. Further, the Caputo-type MSM fractional order differentiation for the incomplete I-functions is studied and investigated. Saigo, Riemann–Liouville, and Erdélyi–Kober fractional operators are also discussed as specific cases.

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::26102f3a181093bf8fcb39f4a3a33c36
http://link.springer.com/article/10.1186/s13662-020-02725-7

المؤلفون: Amit Mathur, Sanjay Bhatter, Jagdev Singh, Devendra Kumar

المصدر: International Journal of Applied and Computational Mathematics. 7

مصطلحات موضوعية: Class (set theory), Pure mathematics, Overline, Applied Mathematics, Order (ring theory), Function (mathematics), Extension (predicate logic), 01 natural sciences, 010305 fluids & plasmas, Fractional calculus, 010101 applied mathematics, Computational Mathematics, Special functions, Product (mathematics), 0103 physical sciences, 0101 mathematics, Mathematics

الوصف: Fractional order calculus and special functions play a great role in scientific, financial and technological fields. In view of considerable impact and applications of fractional derivatives and integrals in real life, we aim to suggest some main formulas for the product of generalized M-series, $${\overline{\text{H}}}$$ -function and Aleph function associated with the Riemann-Liouvillle, the Weyl and many other operators of fractional order, which are derived by using the concept of the Cauchy-Goursat integral formula. The formulas derived in the present study can be employed to examine a broad class of new and known formulas involving simpler special functions, hitherto scattered in the literature.

URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_________::9d572f86b1725dc795e38a7eb20aa129
https://doi.org/10.1007/s40819-021-01007-4