Research Interests

Exploring the mathematical foundations of real-world phenomena through boundary value problems and fractional calculus.

01

Free boundary problems

02

Neumann boundary conditions

03

Elliptic PDEs

04

Regularity/continuity of free boundaries

05

Existence/uniqueness

06

Fractional calculus

07

Fractional differential equations

08

Fractional Sobolev spaces

09

Functional analysis

010

Topology

011

Soft set theory

Key Equations

Lu=−div(A(x)∇u)+c(x)u=f(x)\mathcal{L}_u = -\text{div}(A(x)\nabla u) + c(x)u = f(x)
Dtαf(t)=1Γ(1−α)ddt∫0t(t−τ)−αf(τ)dτD_t^\alpha f(t) = \frac{1}{\Gamma(1-\alpha)} \frac{d}{dt} \int_0^t (t-\tau)^{-\alpha} f(\tau) d\tau