Homotopy perturbation transform method for solving fractional partial differential equations with proportional delay

Abstract

Abstract. This paper deals the implementation of homotopy perturbation transform method (HPTM) for numerical computation of initial valued autonomous system of time-fractional partial differential equations (TFPDEs) with proportional delay, including generalized Burgers equations with proportional delay. The HPTM is a hybrid of Laplace transform and homotopy perturbation method. To confirm the efficiency and validity of the method, the computation of three test problems of TFPDEs with proportional delay presented. The proposed solutions are obtained in series form, converges very fast. The scheme seems very reliable, effective and efficient powerful technique for solving various type of physical models arising in sciences and engineering.

Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay

“…The approximate AVIM solution for = 1 is reported in Table 2. This confirms that the proposed results agreed well with solutions obtained by DTM and RDTM [44], HPM [17], and HPTM [49] and approach the exact solutions.…”

“…The solution behavior of ( , ) for different values of = 0.8, 0.9, 1.0, at different time levels ≤ 1 with = 1, is depicted in Figure 5, whereas two dimensional plots are depicted in Figure 6. Thus, the proposed results agreed well with solutions obtained by HPM [17] and HPTM [49]. For = 1, solution (29) reduces to…”

“…which is same as obtained by DTM and RDTM [44] and HPTM [49] and is a closed form of the exact solution ( , ) = 2 exp( ). The approximate AVIM solution for = 1 is reported in Table 2.…”

“…International Journal of Differential Equations which is closed form to the exact solution and the results due to Sakar et al [17] and Singh and Kumar [49]. The solution behavior of ( , ), taking first six terms, for different values of = 0.8, 0.9, 1.0 at different time levels ≤ 1 with = 1, is depicted in Figure 1…”

“…The solution of problem (21) leads to ( , ) = 0 ( , ) + 1 ( , ) + 2 ( , ) + 3 ( , ) + ⋅ ⋅ ⋅ (24) which is closed form to the exact solution and the results due to Sakar et al [17] and Singh and Kumar [49]. The solution behavior of ( , ) for different values of = 0.8, 0.9, 1.0 at different time levels ≤ 1 with = 1 is depicted in Figure 3, whereas two dimensional plots are depicted in Figure 4.…”