TWO-DIMENSIONAL FRACTIONAL EULER POLYNOMIALS METHOD FOR FRACTIONAL DIFFUSION-WAVE EQUATIONS

S. Raja Balachandar, S. G. Venkatesh, K. Balasubramanian and D. Uma
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S. Raja Balachandar: Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur 613401, Tamil Nadu, India
S. G. Venkatesh: Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur 613401, Tamil Nadu, India
K. Balasubramanian: ��Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam, Tamil Nadu, India
D. Uma: Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur 613401, Tamil Nadu, India

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-15

Abstract: This paper suggests using fractional Euler polynomials (FEPs) to solve the fractional diffusion-wave equation in Caputo’s sense. We present the fundamental characteristics of Euler polynomials. The method for building FEPs is discussed. By basically converting fractional partial differential equations into a system of polynomial equations, these qualities enable us to come near to solving the original problem. A conventional numerical method is then used to solve the resulting system of equations. Theoretical analysis for our proposed strategy is also established, including the convergence theorem and error analysis. The proposed technique’s error bound is confirmed for the test problems as well. The method’s applicability and validity are examined using a variety of instances. The acquired solution is contrasted with other approaches’ solutions described in the literature. This method is better in terms of implementation, adaptability and computing efficiency for solving other partial differential equations as a result of the comparison of the proposed method to existing methods used to solve the fractional diffusion-wave equation.

Keywords: Fractional Euler Polynomial; Caputo Fractional Derivative; Time–Space Fractional Diffusion; Fractional-Order Legendre Functions; Approximate Solutions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400583

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