In this paper, we solve the quadratic -Functional equations 2f(x) + 2f(y) = f(x + y) +  􀀀 2f( (x 􀀀 y)); (0. 1) where  is a  xed non-Archimedean number with  􀀀 2 6= 3. Using the  xed point method and the direct method, we prove the Hyers-Ulam stability of the Functional equation (0. 1) in non-Archimedean Banach spaces.

In this paper, we prove the existence and uniqueness results to the random fractional Functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of a nonlinear additive Functional equation in RNS.

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In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy Functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.

In this paper,  we have improved some of the results in [C. Choi and   B. Lee, Stability of Mixed Additive-Quadratic and Additive--Drygas Functional equations. Results Math.  75  no. 1 (2020), Paper No. 38]. Indeed, we investigate the Hyers-Ulam stability problem of the following   Functional equations\begin{align*}  2\varphi(x + y) + \varphi(x - y) &= 3\varphi(x)+ 3\varphi(y)  \\  2\psi(x + y) + \psi(x - y) &= 3\psi(x) + 2\psi(y) + \psi(-y).\end{align*}We also consider the Pexider type Functional equation \[2\psi(x + y) + \psi(x - y) = f(x) + g(y),\] and the additive Functional equation\[2\psi(x + y) + \psi(x - y) = 3\psi(x) + \psi(y).\]

We consider second order hyperbolic equations with unbounded operator’s coefficients possessing time dependent domain of definition in a Hilbert space. Existence and uniqueness of the strong generalized solution are studied. The proofs rely on a generalization of the well known energy integral method. First, we derive a priori estimates for the strong generalized solutions with the help of Yosida operator approximation. Then, using previous results, we show that the range of the operators generated by the posed problem is dense.