Abstract
The present study introduces a new version of homotopy perturbation method for the solution of system of fractional-order differential equations. In this approach, the solution is considered as a Taylor series expansion that converges rapidly to the nonlinear problem. The systems include fractional-order stiff system, the fractional-order Genesio system, and the fractional-order matrix Riccati-type differential equation. The new approximate analytical procedure depends only on two components. Comparing the methodology with some known techniques shows that the present method is relatively easy, less computational, and highly accurate.
Highlights
Fractional differential equations have received considerable interest in recent years and have been extensively investigated and applied for many real problems which are modeled in different areas
The present study introduces a new version of homotopy perturbation method for the solution of system of fractional-order differential equations
The NHPM for solving system of fractional-order differential equations are based on two component procedure and polynomial initial condition
Summary
Fractional differential equations have received considerable interest in recent years and have been extensively investigated and applied for many real problems which are modeled in different areas. One possible explanation of such unpopularity could be that there are multiple nonequivalent definitions of fractional derivatives 1. The homotopy perturbation method is a powerful devise for solving nonlinear problems. This method was introduced by He 7–9 in the year 1998. In this method, the solution is considered as the summation of an infinite series that converges rapidly. The new homotopy perturbation method NHPM was applied to linear and nonlinear ODEs. In this paper, we construct the solution of system of fractional-order differential equations by extending the idea of 17, 18. Dαi yi t Fi t, y1, y2, y3, . . . , yn fi t , yi t0 ci, 0 < αi ≤ 1, i 1, 2, . . . , n
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