A new and eﬃcient numerical algorithm to solve fractional boundary value problems

Muhammad  Arshad; Samia Bushnaq; Hassan  Khan; Qasim  Khan; Evren  HINCAL

doi:10.5269/bspm.75377

Muhammad Arshad
Samia Bushnaq Princess Sumaya University for Technology
Hassan Khan
Qasim Khan
Evren HINCAL

Résumé

In this paper, we developed a new numerical technique based on Lagrange interpolation polynomials to obtain the solutions of fractional higher order nonlinear boundary value problems. The newly established method is named the Lagrange Interpolation Transform Method (LITM). The fractional derivatives are represented by the Caputo operator. The validity of the proposed technique is conﬁrmed with the help of illustrative examples. The exact and LITM solutions are compared by using graphs and tables, which show the closed contact between the actual and LITM solutions. The results of the suggested technique are compared with the solutions of the Chebyshev wavelet
method (CWM) and the Optimal Homotopy asymptotic method (OHAM). The comparison has shown that the LITM has better accuracy as compared to the CWM and OHAM solutions. The fractional order solutions are investigated, which are convergent towards integer order solutions of the targeted problems. Moreover, the present technique has a straightforward and simple procedure to solve both fractional and integer order problems. The computational work is correctly done with the help of MAPLE software and requires less CPU time. The present method can be used directly to solve the problems expressed in tabular form, which conﬁrms the novelty of LITM.

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