This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Lapl...

All microprocessor based electronic systems are designed as repetition of finite time activities. The classical infinite Laplace transform (ILT) theory violates this fundamental requirement of engineering systems. We show that this theory assumes that all signals must exist over the entire infinite time interval. Since in engineering this infinite time assumption is not meaningful, this paper p...

Many mathematical models describe the Corona virus disease 2019 (COVID-19) outbreak; however, they require advance skills. The need for this study is to determine diffusion of COVID-19 vaccine in humans. To end, we first establish a Pythagorean fuzzy partial fractional differential equation using integral transforms express effects vaccination on humans under generalized Hukuhara conditions. We...

This article discusses an iterative transformation method via fuzziness that mixtures the Laplace transform with method. Using Caputo derivative operator, proposed technique demonstrates inherent reliability of fractional fuzzy biological population equations initial conditions. The obtained results to are more general and apply a broad variety problems. A parametric description solutions is by...

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

Keywords: Black–Scholes equation Completely monotonic function Finite difference scheme Laplace Transform M-Matrix Positivity-preserving Post–Widder formula a b s t r a c t In this paper we explore discrete monitored barrier options in the Black–Scholes framework. The discontinuity arising at each monitoring data requires a careful numerical method to avoid spurious oscillations when low volati...

Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is presented. ILTM is a combination of Laplace transform method and Iterative method to solve spaceand timefractional telegraph equations. The fractional derivatives are considered in Caputo sense. Closed form analytical expressions are derived in terms of the Mittag-Leffler functions. An illustrative...

In this paper, a Laplace transform decomposition algorithm (LTDA) is proposed to solve the Riccati equation. Comparisons are made among the homotopy perturbation method (HPM), the Adomian decomposition method (ADM) and the proposed method. It is shown that the homotopy perturbation method with a specific convex homotopy is equivalent to the Adomian decomposition method and the Laplace transform...