• Ghuge Vijaymala Tanaji
• Dr. Holambe T. L.

This abstract presents a comprehensive exploration of numerical techniques for solving space-fractional Radon diffusion equations (SFRDEs). SFRDEs are prominent mathematical models extensively used in various fields, including physics, engineering, and finance, to describe phenomena characterized by anomalous diffusion processes. In this study, we delve into the challenges posed by these equations due to their non-local and non-linear nature, necessitating sophisticated numerical methodologies for their solution. We focus on finite difference methods, spectral methods, and meshless methods, providing a comparative analysis of their efficacy, accuracy, and computational efficiency in handling SFRDEs. Additionally, we investigate the implementation of fractional calculus operators within these numerical schemes, elucidating their impact on solution accuracy and stability. We discuss practical considerations such as boundary conditions, grid refinement strategies, and computational resources optimization to enhance the performance of numerical algorithms in solving SFRDEs. Through extensive numerical experiments and case studies, we demonstrate the applicability and robustness of the proposed methodologies in accurately capturing the complex dynamics governed by space-fractional Radon diffusion equations. Our findings not only contribute to advancing the theoretical understanding of fractional diffusion processes but also offer valuable insights for practical applications in diverse interdisciplinary fields. This research serves as a foundation for further investigations into more intricate fractional differential equations and paves the way for the development of efficient numerical tools for modelling and simulating anomalous diffusion phenomena in real-world systems.

Space-fractional diffusion equation, Radon diffusion, Fractional calculus, Finite difference method, Finite element method.

"Introducing Solution for Space-Fractional Radon Diffusion Equations", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 8, page no.e434-e444, August-2024, Available :http://www.jetir.org/papers/JETIR2408442.pdf

"Introducing Solution for Space-Fractional Radon Diffusion Equations", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 8, page no. ppe434-e444, August-2024, Available at : http://www.jetir.org/papers/JETIR2408442.pdf