Remarks on a New Variable-Coefficient Integro-Differential Equation via Inverse Operators - Chenkuan Li; Nate Fingas; Ying Ying Ou (Fractal and Fractional)
In this paper, we investigate functional inverse operators associated with a class of fractional integro-differential equations. We further explore the existence, uniqueness, and stability of solutions to a new integro-differential equation featuring variable coefficients and a functional boundary condition. To demonstrate the applicability of our main theorems, we provide several examples in which we compute values of the two-parameter Mittag–Leffler functions. The proposed approach is particularly effective for addressing a wide range of integral and fractional nonlinear differential equations with initial or boundary conditions—especially those involving variable coefficients, which are typically challenging to treat using classical integral transform methods. Finally, we demonstrate a significant application of the inverse operator approach by solving a Caputo fractional convection partial differential equation in <semantics>Rn</semantics> with an initial condition.