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, Page 1-16 PDF (317.05 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2025.362953.1161 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Maged Bin-Saad; Jihad Younis 
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| 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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