eng Science and Education Publishing International Journal of Partial Differential Equations and Applications 2376-9556 2022-12-22 9 1 7 12 10.12691/ijpdea-9-1-2 IJPDEA2022912 article Bhaktaraj Thiyam bhaktarajthiyam3076@gmail.com 1 Konthoujam Ibochouba Singh 2 Md. Indraman Khan 3 Md. Mazhar Ul Haque 4 R.K Pratima Devi 4 Department of Mathematics, Manipur International University, Imphal, India Department of Mathematics, Manipur International University, Imphal Department of Mathematics, PETTIGREW College, Ukhrul, Manipur University Department of Mathematics, MAEERĄ¯s MIT Pune, MIT College, Nanded In this paper, we reviewed the specific tasks involved in solving different mathematical equations or fractional integral. Since solutions for different component of modeling models from various fields such as physics, engineering, chemistry, biological etc. involve special work as part of their solutions, here, we review and include the type and general- ization of such specialized functions. http://pubs.sciepub.com/ijpdea/9/1/2/ijpdea-9-1-2.pdf special functions fractional integral calculus Mittag-Leffler function Fox H-function hyper-Bessel function