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 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.
Highlights
From last three decade the fractional calculus have experienced significant observation to solve the mathematics, science & engineering and mathematical physics problems [1,2,3,4,5,6,7,8,9,10,11]
We study a few important fundamental definitions associated to fractional calculus, Elzaki transform and special function to understand the further results, lemmas and application
We introduce a formula of Elzaki transform of generalized Lorenzo-Hartely function, Hilfer derivative & generalized Lauricella confluent hypergeometric function
Summary
From last three decade the fractional calculus have experienced significant observation to solve the mathematics, science & engineering and mathematical physics problems [1,2,3,4,5,6,7,8,9,10,11]. Fractional calculus plays a vital role to derive the solution of various kinds of differential and integral equations of fractional order arising in fractal geometry, propagation of seismic waves and diffusion problems for these we can cite the following works mentioned in [2,4,11,12,13,14]. In this connection Boyadjiev et al [15] studied the non-homogeneous fractional integro-differential equation of Volterra-type (FIDEV) and obtained the solution in closed form in terms of Kummer functions and incomplete gamma function (IGF). Our objective of this paper is to investigate the formulae of Elzaki transform of functions which have been mentioned earlier and these results will be used to solve the generalized fractional integro-differential equations established here
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
