The Analysis of Fractional‐Order Proportional Delay Physical Models via a Novel Transform

Abstract

In this paper, we deal with an alternative analytical analysis of fractional-order partial differential equations with proportional delay, achieved by applying Yang decomposition method, where the fractional derivative is taken in Caputo sense. The suggested series results are discovered to quickly converge to an exact solution. The computation of three test problems of fractional-order with proportional delay partial differential equations was presented to confirm the validity and efficiency of suggested method. The system appears to be a very dependable, effective, and powerful method for solving a variety of physical problems that arise in engineering and science.

Non-Instantaneous Periodic BVP of Fractional Volterra-Fredholm Models

“…Definition 2.3. A function Ψ ∈ PC(J, Υ) is said to be a PC-mild solution of model (1), if Ψ(ν) satisfies the integral equation…”

“…This mathematical framework is effective for simulating complicated events with non-local and memorydependent behaviours. The theory of FC was crucial in the development of differential equations as a powerful tool for simulating several real-world issues in a variety of scientific domains, including physics, control systems, engineering fields, etc [1,14,20]. Integro-differential equations (IDEs) with instantaneous impulse are unable to fully describe several dynamical difficulties in the evolution process.…”

An analytical approach for Yang transform on fractional-order heat and wave equation

“…Liu et al [24] applied yang transformation and Homotopy perturbation transform along with Caputo derivative on Klein-Gordon equation. Alesemi et al [25] investigated an analytical solution of FPDEs by applying Yang decomposition method on proportional delay. Yasmin [26] introduced the semi-analytical solution of the fractional-order paired system of Whitham-Broer-Kaup equation by applying a method namely Yang transformation coupled with Adomian technique.…”

Novel Evaluation of Fuzzy Fractional Cauchy Reaction-Diffusion Equation

“…Modelling nonlinear schemes of the differential equation give rise to a slew of issues [20][21][22]. Scholars have sought to analyze these issues numerically or analytically using various approaches and formulae to achieve better precision [23][24][25][26]. In numerical analysis, the implicit and explicit Finite Difference Method (FDM), spectral collocation method, subdomain least squares method, Galerkin and modified Galerkin methods, shooting method, and decomposition method are all often employed [27][28][29][30].…”