AN EXTENDED LAPLACE INTEGRAL TRANSFORM AND ITS APPLICATIONS

Shilpi Jain (), Miguel Vivas-Cortez (), Parik Laxmi (), Praveen Agarwal and Shaher Momani
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Shilpi Jain: Department of Mathematics, Poornima College of Engineering, Jaipur 302022, Rajasthan, India
Miguel Vivas-Cortez: Escuela de Ciencias Físicas y Matematicas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Catolica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador
Parik Laxmi: Department of Mathematics, Poornima University, Jaipur, Rajasthan, India
Praveen Agarwal: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE5Department of Mathematics, Anand International College of Engineering, Jaipur 303012, Rajasthan, India6Faculty of Engineering, International Telematic University Uninettuno Corso, Vittorio Emanuele II, 3900186 Roma, Italy7Department of Mathematical Sciences, Saveetha School of Engineering, Chennai 602105, Tamil Nadu, India
Shaher Momani: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE8Department of Mathematics, School of Science, The University of Jordan, Amman 11942, Jordan

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-22

Abstract: In this paper, we introduce a new integral transform, called an extended Laplace integral transform, and also investigate its properties like linearity property, first and second shifting property, change of scale property, convolution theorem, and derivative property. Moreover, we obtain an extended Laplace integral transform of some elementary functions. Furthermore, we demonstrate an extended Laplace integral transform in solving ordinary and partial differential equations through different examples. We also introduce a new application of an extended Laplace integral transform for Volterra integral equations, Volterra integro-differential equations, and Caputo fractional-order differential equations. Finally, by replacing some parameters appropriately, an extended Laplace integral transform is reduced to several integral transforms known in the literature as special cases.

Keywords: An Extended Laplace Integral Transform; Ordinary Differential Equation; Partial Differential Equation; Volterra Integral Equation; Volterra Integro-Differential Equation; and Caputo Fractional-Order Differential Equation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401243

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