Generalized Substantial Fractional Operators and Well-Posedness of Cauchy Problem - Fahad, Hafiz Muhammad; Ur Rehman, Mujeeb (Springernature, 2021)
In this work, we focus on substantial fractional integral and differential operators which play an important role in modeling anomalous diffusion. We introduce a new generalized substantial fractional integral. Generalizations of fractional substantial derivatives are also introduced in both Riemann-Liouville and Caputo sense. Furthermore, we analyze fundamental properties of these operators. Finally, we consider a class of generalized substantial fractional differential equations and discuss the existence, uniqueness and continuous dependence of solutions on initial data.
Keywords: Generalized fractional derivative; Fractional integrals; Caputo derivatives; Riemann-Liouville derivative; Gronwall inequality; Well-posedness