Hossein Jafari 1,2,*, Hassan Kamil Jassim 2,3, Fairouz Tchier 4 and Dumitru Baleanu 5,6 1 Department of Mathematical Sciences, University of South Africa (UNISA), Pretoria 0003, South Africa 2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar 47416, Iran; [email protected] 3 Department of Mathematics, Faculty of Education for Pure Sciences, U...

Abstract Using the framework of random walks in random scenery, Cohen and Samorodnitsky (2006) introduced a family of symmetric α-stable motions called local time fractional stable motions. When α = 2, these processes are precisely fractional Brownian motions with 1/2 < H < 1. Motivated by random walks in alternating scenery, we find a complementary family of symmetric α-stable motions which we...

This study proposed an image enhancing method which is based on the non-local fractional order differential operator. In this method, a matrix form representation of discrete fractional order differentiation is introduced to enhance the digital image, which is effective to reduce the computation error caused by the traditional local approximate method of the fractional order differentiation. Th...