Legendre multiwavelet collocation method for solving the linear fractional time delay systems

Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations

“…It is difficult to find an accurate and analytical solution to this problem, so approximate and numerical methods should be used to solve these problems. Different numerical methods have been used to solve fractional pantograph differential equations such as Hermit wavelets method [8], spectral method [9,10], fractionalorder Bernoulli wavelet method [11], fractional-order Boubaker polynomials [12], Taylor collocation method [13,14], Laguerre-Gauss collocation method [15], Legendre multiwavelet collocation method [16], two-step Runge-Kutta of order one method [17], one-Leg θ method [18], variational method [19], collocation method [20], generalized differential transform scheme [21], modified the predictor-corrector scheme [22], and Bernoulli wavelet method [23].…”

On a new structure of the pantograph inclusion problem in the Caputo conformable setting

“…Indeed, Aphithana, Ntouyas and Tariboon [46] regraded a modern BVP including the Caputo conformable differential equation along with integral conditions: also uniqueness criteria for the proposed problem. After that, different researchers studied fractional pantograph equations with the help of various numerical methods such as the operational method, the spectral-collocation method, and the Hermite wavelet method [49][50][51]. Recently, other researchers investigated various versions of fractional pantograph equations relying on analytical methods (see [52][53][54]).…”