TY - JOUR T1 - Generalized Pathway Fractional Integral Formulas Involving Extended Multi-Index Mittag-Leffler Function in Kernel of SUM Transform AU - Abubakar, Umar Muhammad AU - Kaurangini, Muhammad AU - Ata, Enes PY - 2025 DA - June Y2 - 2025 DO - 10.51354/mjen.1543383 JF - MANAS Journal of Engineering JO - MJEN PB - Kyrgyz-Turkish Manas University WT - DergiPark SN - 1694-7398 SP - 18 EP - 22 VL - 13 IS - 1 LA - en AB - The generalized pathway fractional integral formulas for the newly extended multiindex Mittag-Leffler function defined by using two Fox-Wright functions as its kernel is studied. Moreover, the SUM integral transform of the composition formula for the pathway fractional integral and extended multi-index Mittag-Leffler function is also presented. KW - SUM transform KW - Laplace transform KW - Mittag-Leffler function KW - Pathway fractional integral operator KW - Wright function CR - [1] Singh A., Kumar S., Vigo-Angular, J., On New Approximations of Caputo-Prabhakar Fractional Derivative and their Application to Reaction-diffusion Problems with Variable Coefficients, Mathematical Method in the Applied Sciences 47, (2023), 268-296. CR - [2] Yadav P., Johan S., Shah K., Peter O.M., Fractional-order Modeling and Analysis of Debates Mellitus: Utilizing the Atangana-Baleanu Caputo (ABC) operator, Alexandria Engineering Journal, 81, (2023), 200-209. CR - [3] Kaur, D., A details study on fractional calculus, In: Conference Proceeding of International Multidisplinary Conference, pp. 54-59, 2022. CR - [4] Turkyilmazoglu, M., Altanji, M., ”Fractional Models of Falling Object with Linear and Quadratic Frictional Forces Considering Caputo Derivatives,” Chaos, Solitons and Fractals, 166:112980, 2023. CR - [5] Nair, S.S., Pathway Fractional Integration Operator, Fractional Calculus and Applied Analysis, 12, (2009), 237-259. CR - [6] Nair, D.H., On a class of Fractional Integral Operator through Pathway Ideas, Proceeding of 12𝑡ℎ Annual Conference Society for Special Functions and Their Applications, 12, pp. 91-109, 2013. CR - [7] Pal, A., Jana, R.K., Shukla, A.K., Generalized Integral Transform and Fractional Calculus involving Extended 𝑞𝑅𝑞 (𝛼, 𝛽; 𝑧) Function, Journal of the Indian Mathematical Society, 89, (2022), 100-116. CR - [8] Kaurangini, M.L., Abubakar, U.M., Ata, E., New Extended Multi-index Mittag-Leffler Function and Application of Double Mellin Integral Transform and Riemann-Liouville Fractional Operators, Submitted for Publication, 2024. CR - [9] Kaurangini, M.L., Chaudhary, M.P., Abubakar, U.M., Kiymaz, I.O., Ata, E., On Some Special Functions with Bi-Fox-Wright Function Kernel,” Submitted for Publication 2024. CR - [10] Chaudhary, M.P., M.L. Kaurangini, M.L., Kiymaz, I.O., Abubakar, U.M., Ata, E., Fractional Integrations for the New Generalized Hypergeometric Functions, Journal of Ramanujan Society of Mathematical Science, 10, (2023), 77-100. CR - [11] Ghanim, F., Al-Janaby, H.F., Al-Momani, M., A New Euler-Beta Function Model with Statistical Implementation Related to the Mittag-Leffler-Kumar Function, Kuwait Journal of Science, 2023, (2023), 1-27. CR - [12] Pohlen, T., The Hadamard Product and Universal Power Series, PhD Dissertation, Unviversitat Trier, Trier, Germany, 2009. CR - [13] Hasan, S.Q., Abubakar, U.M., Kaurangini, M.L., The New Integral Transform ”SUM Transform” and its Properties, Palestine Journal Mathematics, 12(2023), 30-45. CR - [14] Hassan,S. Q., Mansour, A.I., Abubakar,U.M., Applications of the SUM Integral Transform in Science and Technolog, Wasit Journal for Pure sciences, 2, (2023), 29-40. CR - [15] Rahman, G., Nisar, K.S., Choi, J., Mubeen, S., Arshad, M., Pathway fractional Integral Formulas involving Extended Mittag-Leffler Functions in the Kernel, Kyungpook Mathematical Journal, 59, (2019), 125-134. CR - [16] Agarwal, P., Akhtar, H.M., Khan, A., Momani, S., Abdel- Aty, M., Pathway Fractional Formula involving Extended Mittag-Leffler Function in the Kernel of Generalized Elzaki Transform, Progress in Fractional Differential and Applications, 9, (2023), 25-32. UR - https://doi.org/10.51354/mjen.1543383 L1 - https://dergipark.org.tr/en/download/article-file/4189860 ER -