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Introducing and solving generalized Black-Scholes PDEs through the use of functional calculus
Jesús Oliva-Maza, Mahamadi Warma
We introduce some families of generalized Black--Scholes equations which involve the Riemann-Liouville and Weyl space-fractional derivatives. We prove that these generalized Black-…
Control and numerical approximation of fractional diffusion equations
Umberto Biccari, Mahamadi Warma, Enrique Zuazua
The aim of this work is to give a broad panorama of the control properties of fractional diffusive models from a numerical analysis and simulation perspective. We do this by survey…
Exponential Turnpike property for fractional parabolic equations with non-zero exterior data
Mahamadi Warma, Sebastian Zamorano
We consider averages convergence as the time-horizon goes to infinity of optimal solutions of time-dependent optimal control problems to optimal solutions of the corresponding stat…
Moreau-Yosida regularization for optimal control of fractional PDEs with state constraints: parabolic case
Harbir Antil, Thomas S. Brown, Deepanshu Verma +1
This paper considers optimal control of fractional parabolic PDEs with both state and control constraints. The key challenge is how to handle the state constraints. Similarly, to t…
Approximate and mean approximate controllability properties for Hilfer time-fractional differential equations
Ernest Aragones, Valentin Keyantuo, Mahamadi Warma
We study the approximate and mean approximate controllability properties of fractional partial differential equations associated with the so-called Hilfer type time-fractional deri…
Convergence of solutions of discrete semi-linear space-time fractional evolution equations
Harbir Antil, Carlos Lizama, Rodrigo Ponce +1
Let be the realization of the fractional Laplace operator on the space of continuous functions , and let denote the discrete fractional Lapla…