Application of the φ,ψ-Double Integral Transform to Particular φ,ψ-Fractional Differential Equations

In this work, we propose a simple analytical/semi-analytical approach to solve various φ,ψ-fractional partial differential equations (φ,ψ-FPDEs) using initial and boundary conditions (ICs, BCs) depending on the φ,ψ-Double Elzaki transform (φ,ψ-DET) method. The suggested approach takes advantage of a DPET modification that works well with φ,ψ-fractional operators. The proposed method not only solves the φ,ψ-FPDEs but also reduces them to a more straightforward algebraic recurrence issue. This simple yet powerful idea can be used to solve φ,ψ-FPDEs in science and engineering. We contrast the outcomes of the stated computational examples with exact solutions in order to verify the exactness and efficacy of this methodology.