An efficient hybridization scheme for time-fractional Cauchy equations with convergence analysis

Saud Fahad Aldosary; Ram Swroop; Jagdev Singh; Ateq Alsaadi; Kottakkaran Sooppy Nisar; Saud Fahad Aldosary; Ram Swroop; Jagdev Singh; Ateq Alsaadi; Kottakkaran Sooppy Nisar

doi:10.3934/math.2023072

AIMS Mathematics

2023, Volume 8, Issue 1: 1427-1454. doi: 10.3934/math.2023072

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An efficient hybridization scheme for time-fractional Cauchy equations with convergence analysis

1.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam bin Abdulaziz University, Saudi Arabia
2.
Department of Mathematics, Arya College of Engineering and IT, Kukas, Jaipur, Rajasthan 302028 India
3.
Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India
4.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 10 May 2022 Revised: 31 August 2022 Accepted: 06 September 2022 Published: 20 October 2022
MSC : 34A08, 35A20, 35A22, 35C05

In this paper, a time-fractional Cauchy equation (TFCE) is analyzed by using the q-homotopy analysis Shehu transform algorithm (q-HASTA) with convergence analysis. The q-HASTA comprises with the reduced differential transform algorithm (RDTA). The solution of TFCE is represented in the series form by using the q-HASTA scheme. The TFCE is transformed into algebraic form for finding the general solution efficiently. This provides a compact form solution with minimized error. There are three key outcomes of the work. First, the small size of input parameters by the RDTA transforms into the subsidiary equation so that it takes short time to solve. As the second advantage, the structure of the problem is reduced by controlling the solution series; hence the characterization of the solution becomes classified for finding the particular solution. The third advantage of this work is that the approximate solution with absolute error approximation for the fractional model of the problem is handled by using a generalized and efficient scheme q-HASTA. These outcomes are illustrated by graphs and tables.
Citation: Saud Fahad Aldosary, Ram Swroop, Jagdev Singh, Ateq Alsaadi, Kottakkaran Sooppy Nisar. An efficient hybridization scheme for time-fractional Cauchy equations with convergence analysis[J]. AIMS Mathematics, 2023, 8(1): 1427-1454. doi: 10.3934/math.2023072

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Abstract

In this paper, a time-fractional Cauchy equation (TFCE) is analyzed by using the q-homotopy analysis Shehu transform algorithm (q-HASTA) with convergence analysis. The q-HASTA comprises with the reduced differential transform algorithm (RDTA). The solution of TFCE is represented in the series form by using the q-HASTA scheme. The TFCE is transformed into algebraic form for finding the general solution efficiently. This provides a compact form solution with minimized error. There are three key outcomes of the work. First, the small size of input parameters by the RDTA transforms into the subsidiary equation so that it takes short time to solve. As the second advantage, the structure of the problem is reduced by controlling the solution series; hence the characterization of the solution becomes classified for finding the particular solution. The third advantage of this work is that the approximate solution with absolute error approximation for the fractional model of the problem is handled by using a generalized and efficient scheme q-HASTA. These outcomes are illustrated by graphs and tables.

References

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