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Keywords = Elazki transform

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11 pages, 279 KB  
Article
On the Volterra-Type Fractional Integro-Differential Equations Pertaining to Special Functions
by Yudhveer Singh, Vinod Gill, Jagdev Singh, Devendra Kumar and Kottakkaran Sooppy Nisar
Fractal Fract. 2020, 4(3), 33; https://doi.org/10.3390/fractalfract4030033 - 9 Jul 2020
Cited by 3 | Viewed by 3097
Abstract
In this article, we apply an integral transform-based technique to solve the fractional order Volterra-type integro-differential equation (FVIDE) involving the generalized Lorenzo-Hartely function and generalized Lauricella confluent hypergeometric function in terms of several complex variables in the kernel. We also investigate and introduce [...] Read more.
In this article, we apply an integral transform-based technique to solve the fractional order Volterra-type integro-differential equation (FVIDE) involving the generalized Lorenzo-Hartely function and generalized Lauricella confluent hypergeometric function in terms of several complex variables in the kernel. We also investigate and introduce the Elazki transform of Hilfer-derivative, generalized Lorenzo-Hartely function and generalized Lauricella confluent hypergeometric function. In this article, we have established three results that are present in the form of lemmas, which give us new results on the above mentioned three functions, and by using these results we have derived our main results that are given in the form of theorems. Our main results are very general in nature, which gives us some new and known results as a particular case of results established here. Full article
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