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On the Fractional Differential Equations Associated with Integral Operator Involving Aleph Function in the Kernel |
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PP: 665-679 |
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doi:10.18576/pfda/090410
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Author(s) |
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Yudhveer Singh,
Vinod Gill,
Jagdev Singh,
Monika Jain,
Devendra Kumar,
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Abstract |
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| In the present article, we introduced and explore an integral operator which consist Aleph function in the kernel with fractional calculus. In second section, we construct the characteristics of R-L fractional integral operator Iβ and derivative operator
Dβa+ containing the Aleph-function and in third section, we develop the Sumudu transform of propose integral operator. In fourth section, we find the solutions of arbitrary order differential equations which consists the Hilfer derivative operator along with propose integral operator by applying Sumudu transform. We also established some fascinating corollaries and particular cases of our key results presented here in terms of a number of special functions particularly H-function, I-function, Mittag-Leffler, and generalized Bessel- Maitland function and exhibit to be their relation with certain known results. In the end of the article, we develop some graphical results to show the behavior of differential equation by assigning particular values to the parameters.
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