Abstract
In this paper, three numerical schemes are formulated for generalized isoperimetric constraint fractional variational problems (GICFVPs) described using the generalized fractional derivative (GFD). The GFDs involve the concept of scale and weight functions. Three numerical schemes, i.e. linear, quadratic, and quadratic-linear schemes are developed to get numerical solutions of a GICFVP. The error analysis of the schemes is also presented in detail. The convergence rate of the linear and quadratic schemes are estimated as \(2-\alpha\) and \(3-\alpha\), \(\alpha \in (0,1)\) respectively. It is observed that the presented schemes perform well, and when the step size \(\text{h}\) is decreased, the desired solution is attained. We present results for different scale and weight functions in GFD varying \(\alpha\) to show the significance of the schemes. Moreover, we too explain the consequences of scale and weight functions on numerical results of quadratic type GICFVPs. The precision of the numerical techniques concerning different weight and scale functions, and parameters such as \(\alpha\) and \(\text{h}\) is examined and demonstrated in detail through figures and tables.
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Pandey, D., Kumar, K. & Pandey, R.K. Approximation schemes for a quadratic type generalized isoperimetric constraint fractional variational problems. J Anal 32, 191–218 (2024). https://doi.org/10.1007/s41478-023-00619-x
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DOI: https://doi.org/10.1007/s41478-023-00619-x