Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

Abstract

We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples.

Generalized model of stochastic common property fishery differential game: Numerical study

“…. , N ) is a feedback Nash equilibrium solution for the problem (1) subject to (2), if there exist the value functions W i (x), i = 1, 2, . .…”

“…From a modelling point of view, a generalized model refers to a model that can be applied to various scenarios and provides a more comprehensive understanding or prediction of the underlying phenomena. For instance, the natural growth function ax(τ) 1 2 − bx(τ) in (2) can be changed because of births, deaths, immigrations and emigrations. However, it is important to note that this natural growth function is a simplified model and may not accurately represent real-world complexities and limitations.…”

“…Abdelkawy et al [1] used FLFs to solve the nonlinear systems of variable order fractional Fredholm integro-differential equations. Similar to FLFs, the fractional-order shifted Jacobi functions have been constructed in Abdelkawy et al [2] employed to find the approximate solution of variable-order fractional integro-differential equations. Also, the fractional-order hybrid of block-pulse functions and Bernoulli polynomials in Postavaru, and Toma [45] was considered for solving two-dimensional fractional order equations.…”

A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a Quadrature Nystrom Method

“…Using the extended cubic B-spline, Akram et al [17] interpreted the collocation strategy in order to solve the fractional partial integro-differential problem. After employing the Riemann-Liouville fractional integral and fractional derivative, Abdelkawy et al [18] used the Jacobi-Gauss collocation method to achieve an approximate solution for a variable-order of FrLIoDE with a weakly singular kernel. This was accomplished by applying the Jacobi-Gauss collocation method.…”