A Generalized Fractional Integral Transform for Solutions of Fractional Burger’s Equation

Abstract

This paper introduces a novel fractional-order integral transform within the field of fractional calculus and applies it to the solution of fractional burger’s equation with different fractional differential operator. In this study, we apply the newly proposed transform to several fractional differential, including Caputo, Caputo-Fabrizio, RiemannLiouville, New Fractional Derivative and Atangana-Baleanu operators in both the Riemann-Liouville and Caputo senses. For varying values of ϕ α(s), ψ(s) and γ(t), the over 200 existing integral transforms and fractional integral transforms can be considered special cases of the proposed transform when applied to the aforementioned derivatives. This suggests the versatility and applicability of our newly introduced fractional-order integral transform within the broader context of fractional calculus, engineering and physics. The analytical solution of Fractional order Viscous Burger’s equation with different differential and integral operators are also discussed.