Analysis of random fractional order differential equations with Shehu analysis transformation method

This thesis examines fractional order ordinary and partial differential equations, together with their systems incorporating random parameters, utilizing the Shehu analysis transformation method for their resolution. The Shehu analysis transformation method is beneficial due to its streamlined process stages relative to other transformation approaches and its ability to yield convergent findings rapidly.Initially, the paper presented the definition and characteristics of the Caputo-Fabrizio fractional order derivative, the formulation of the random Bagley-Torvik type equation, and the inverse Shehu transformation technique. The coefficients or beginning conditions were derived from continuous probability distributions, including Normal, Uniform, Exponential, Triangular, Beta, Erlang, and Gamma distributions, and the equations were randomized. Approximate analytical solutions for fractional-order ordinary and partial differential equations with random initial conditions or coefficients were derived and the expected values, variance, and confidence intervals of these solutions were calculated. The corresponding graphs of the derived solutions were found using Matlab or Maple software packages program.The results indicate that the Shehu analysis transformation method is an effective, rapid, and dependable approach for analytical and approximation solutions of ordinary and partial differential equations, as well as systems of arbitrary fractional order. This paper significantly contributes to the domain of applied mathematics.