Abstract
Abstract Novel results on conformable Bessel functions are proposed in this study. We complete this study by proposing and proving certain properties of the Bessel functions of first order involving their conformable derivatives or their zeros. We also establish the orthogonality of such functions in the interval [0,1]. This study is essential due to the importance of these functions while modeling various physical and natural phenomena.
Highlights
Fractional calculus is theoretically a powerful analysis technique for investigating arbitrary order integrals and derivatives. This field of research has been only presented purely, and until very recently, researchers have realized the powerful applicability of this field in modeling many phenomena from natural sciences and engineering much better than using the ordinary usual calculus due to several properties in fractional calculus that can provide a good explanation of physical behavior of certain system
The applications of conformable and fractional calculus have been recently discussed in some research studies [8,9,10,11,12,13,14,15]
The analysis of conformable derivatives and integrals has been discussed in detail in earlier studies [16,17]
Summary
Fractional calculus is theoretically a powerful analysis technique for investigating arbitrary order integrals and derivatives. At the beginning, this field of research has been only presented purely, and until very recently, researchers have realized the powerful applicability of this field in modeling many phenomena from natural sciences and engineering much better than using the ordinary usual calculus due to several properties in fractional calculus that can provide a good explanation of physical behavior of certain system
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