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    A Note on Hyperbolic Differential Equations on Manifold
    (Amer Inst Physics, 2021) Ashyralyev, Allaberen; Sozen, Yasar; Hezenci, Fatih
    In this extended abstract, considering the differential equations on hyperbolic plane. we investigate and establish the well-posedness of boundary value problem for hyperbolic equations in Holder spaces. Furthermore, we establish new coercivity estimates in various Holder norms for the solutions of such boundary value problems for hyperbolic equations.
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    A Note on Parabolic Differential Equations on Manifold
    (Amer Inst Physics, 2021) Ashyralyev, Allaberen; Sozen, Yasar; Hezenci, Fatih
    The present extended abstract considers the differential equations on smooth closed manifolds, investigates and establishes the well-posedness of nonlocal boundary value problems (NBVP) in Holder spaces. It also establishes new coercivity estimates in various Holder norms for the solutions of such boundary value problems for parabolic equations.
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    Numerical approaches for solution of hyperbolic difference equations on circle
    (Walter De Gruyter Gmbh, 2024) Ashyralyev, Allaberen; Hezenci, Fatih; Sozen, Yasar
    The present paper considers nonlocal boundary value problems for hyperbolic equations on the circle T-1 . The first-order modified difference scheme for the numerical solution of nonlocal boundary value problems for hyperbolic equations on a circle is presented. The stability and coercivity estimates in various Holder norms for solutions of the difference schemes are established. Moreover, numerical examples are provided.