Abstract
In this paper, we investigate the fractional derivatives and expansion formulae of incomplete $H$ and $\overline{H}$-functions for one variable. Further, we also obtain results for repeated fractional order derivatives and some special cases are also discussed. Various other analogues results are also established. The results obtained here are very much helpful for the further research and useful in the study of applied problems of sciences, engineering and technology.
Highlights
Introduction and PreliminariesThe fractional derivative from Oldham and Spanier [12] of complex order α of a function f (t) is dened by βDαt [f (t)] =1 Γ(−α) βt(t − x)−α−1f (x)dx, (α) < 0, dm dxm ·βDαt −m {f (t)}, 0 ≤ (α) < m, (1)where m ∈ I+(Positive integer)
We found from the results for recurrent and repeated fractional order derivatives and discussed about their some special cases
The results obtained here are very much helpful for the further research and useful in the study of applied problems of sciences, engineering and technology
Summary
Nirmal Kumar Jangida, Sunil Joshia, Sunil Dutt Purohitb, Daya Lal Sutharc aDepartment of Mathematics & Statistics, Manipal University Jaipur, Jaipur, India. bDepartment of HEAS (Mathematics), Rajasthan Technical University, Kota, India. cDepartment of Mathematics, Wollo University, P.O. Nirmal Kumar Jangida, Sunil Joshia, Sunil Dutt Purohitb, Daya Lal Sutharc aDepartment of Mathematics & Statistics, Manipal University Jaipur, Jaipur, India. BDepartment of HEAS (Mathematics), Rajasthan Technical University, Kota, India. CDepartment of Mathematics, Wollo University, P.O. Box: 1145, Dessie, Ethiopia
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