Fractional calculus formulas for extended Mittag-Leffler-type function of arbitrary order using Marichev-Saigo-Maeda operators | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 16, Issue 2, 2025, Pages 1-16 PDF (317.05 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2025.362953.1161 | ||
| Authors | ||
| Maged Bin-Saad; Jihad Younis* | ||
| Department of Mathematics, Aden University, Aden, Yemen | ||
| Abstract | ||
| Several fractional calculus operators have been introduced and studied. We aim to present the Marichev-Saigo-Maeda fractional integration and differentiation of the extended Mittag-Leffler-type function of arbitrary order. The Caputo-typ Marichev-Saigo-Maeda fractional derivatives are considered for the extended Mittag-Leffler-type function of arbitrary order. As special cases, the corresponding assertions for the Saigo, Erd´elyi–Kober and Riemann–Liouville fractional operators are also deduced.Several fractional calculus operators have been introduced and studied. We aim to present the Marichev-Saigo-Maeda fractional integration and differentiation of the extended Mittag-Leffler-type function of arbitrary order. The Caputo-typ Marichev-Saigo-Maeda fractional derivatives are considered for the extended Mittag-Leffler-type function of arbitrary order. As special cases, the corresponding assertions for the Saigo, Erd´elyi–Kober and Riemann–Liouville fractional operators are also deduced.Several fractional calculus operators have been introduced and studied. We aim to present the Marichev-Saigo-Maeda fractional integration and differentiation of the extended Mittag-Leffler-type function of arbitrary order. The Caputo-typ Marichev-Saigo-Maeda fractional derivatives are considered for the extended Mittag-Leffler-type function of arbitrary order. As special cases, the corresponding assertions for the Saigo, Erd´elyi–Kober and Riemann–Liouville fractional operators are also deduced. | ||
| Keywords | ||
| Fox-Wright function; extended Mittag–Leffler function; operators of fractional calculus | ||
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