A new Rabotnov fractional‐exponential function‐based fractional derivative for diffusion equation under external force. (14th January 2020)

• Record Type: Journal Article
• Authors: Kumar, Sunil; Nisar, Kottakkaran Sooppy; Kumar, Ranbir; Cattani, Carlo; Samet, Bessem
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 7(2020)
• Page Start: 4460
• Page End: 4471
• Publication Date: 2020-01-14
• Subjects: fractional diffusion equation -- homotopy perturbation method -- Laplace transform method -- new fractional derivative based on sinc function and Rabotnov fractional‐exponential function; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6208
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This work suggested a new generalized fractional derivative which is producing different kinds of singular and nonsingular fractional derivatives based on different types of kernels. Two new fractional derivatives, namely Yang‐Gao‐Tenreiro Machado‐Baleanu and Yang‐Abdel‐Aty‐Cattani based on the nonsingular kernels of normalized sinc function and Rabotnov fractional‐exponential function are discussed. Further, we presented some interesting and new properties of both proposed fractional derivatives with some integral transform. The coupling of homotopy perturbation and Laplace transform method is implemented to find the analytical solution of the new Yang‐Abdel‐Aty‐Cattani fractional diffusion equation which converges to the exact solution in term of Prabhaker function. The obtained results in this work are more accurate and proposed that the new Yang‐Abdel‐Aty‐Cattani fractional derivative is an efficient tool for finding the solutions of other nonlinear problems arising in science and engineering.