A novel approach to fractional differential equations via JSN transform coupled fractional residual power series method

Abstract

In this study, we introduce a novel modified general integral transform known as the JSN transform, which offers several advantages over the Laplace and other integral transforms with exponential kernels. Fundamental results of the JSN transform of the Caputo fractional derivative are discussed. Furthermore, we develop a novel hybrid technique called the JSN Fractional Residual Power Series
Method (JSN FRPSM). This new technique incorporates the JSN transform with the existing Residual Power Series Method. To demonstrate the efficiency of the proposed hybrid technique in solving fractional differential equations, we apply it to various fractional differential equations encountered in science and engineering. Statistical and error analyses are conducted to validate the results obtained through the proposed method. Additionally, the series solutions obtained via the
proposed method are illustrated graphically.