Fractional infimal and supermal convolutions with applications | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 33, Issue 1, 2025, Pages 83-97 PDF (416.88 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/joems.2025.410188.1054 | ||
| Authors | ||
| Hany El Deeb* ; Nashat Faried; Hewayda Lotfy; Rabab Mostafa | ||
| Abbassia | ||
| Abstract | ||
| In this paper, we introduce the notions of p-infimal convolution (p-ic) and p-supermal convolution (p-sc) , where p is a fraction lies between 0 and 1 , as an extension of infimal and supermal convolutions and verify that these operations are commutative and associative for any p. Meanwhile, we show that the (p-ic)increases with p while the (p-sc) decreases and notice that when applying the (p-ic) for a certain function several times we get a sub-addatitive function while applying the supermal convolution several times we get a super-additive function. Also, we extend the convolution of two functions to p-convolution, which helps us to find Laplace transform for many functions and give some applications for our results. We present a solution of a Volterra integral equation in the p form. The fractional convolution of two functions f,g plays an important role in several different physical applications.Also, we introduce Fractional Convolution Theorem with some examples | ||
| Keywords | ||
| convolution; infimal convolution; supermal convolution | ||
|
Statistics Article View: 3 PDF Download: 7 |
||
