Growth estimates of solutions to fractional hybrid partial differential equations

Abstract

We investigate a class of fractional hybrid partial differential equations subject to both linear and quadratic perturbations. By imposing a Lipschitz continuity condition on the third variable of the non-linear functions, we establish the well–posedness of the equations’ solutions by applying the Banach fixed–point theorem. The growth estimates of solutions to these perturbation equations are derived using the non-linear weakly singular fractional integral inequality of the Wendroff type. Additionally, the growth behaviors for both types of equations are analyzed, and the result shows that they exhibit some exponential growth rates. It is further noted that the proofs of the equations’ properties entail varying degrees of difficulty and requiring additional conditions. Several numerical examples are presented to provide insights and highlight the significance of our results.