A NOVEL TEMPERED FRACTIONAL TRANSFORM: THEORY, PROPERTIES AND APPLICATIONS TO DIFFERENTIAL EQUATIONS

Sayed Saifullah, Amir Ali (), Arshad Khan, Kamal Shah and Thabet Abdeljawad
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Sayed Saifullah: Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK 18000, Pakistan
Amir Ali: Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK 18000, Pakistan
Arshad Khan: Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK 18000, Pakistan
Kamal Shah: Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK 18000, Pakistan†Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Thabet Abdeljawad: ��Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia‡Department of Medical Research, China Medical University, Taichung 40402, Taiwan§Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea¶Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-14

Abstract: In this paper, we develop a new technique known as Tempered Fractional ð • -Transform (TFð • T). This scheme can be applied to study numerous linear and nonlinear dynamical systems in tempered fractional (TF) calculus in both Riemann–Liouville and Caputo and sense. Some new theories, properties, and applications of the above-mentioned ð • -transform are calculated in detail. The proofs of some important theorems on TF Riemann–Liouville and Caputo derivatives are proved based on TFð • T. For validation, accuracy and efficiency, the general TF equations as well as TF linear and nonlinear Klein–Gordon equations are studied by using the proposed transform with the numerical illustrations. It is observed that the proposed technique is fast convergent and the results are the first precise confirmations of TFð • T in tempered calculus for nonlinear systems. This work can be studied as a substitute to present mathematical methods and will have extensive applications in physical sciences.

Keywords: ð • -Transform; Riemann–Liouville Derivative; Caputo Derivative; Tempered Fractional Calculus; Tempered Fractional Linear and Nonlinear Klein–Gordon Equations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400455

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