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Journal of Applied Nonlinear Dynamics 12(3) (2023) 537--545 | DOI:10.5890/JAND.2023.09.008

R. Dhineshbabu$^1$, A. George Maria Selvam$^2$

$^1$ Department of Mathematics, Sri Venkateswara College of Engineering and Technology (Autonomous), Chittoor - 517 127, Andhra Pradesh, India

$^2$ Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur - 635 601, Tamil Nadu, India

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Abstract

Boundary value problems have wide applications in science and technology. In this paper, one dimensional heat equation model together with initial and Neumann boundary conditions are presented and we compute the steady state solutions of our concerned problem. Furthermore, we discuss various kinds of Ulam stability analysis for the nonlinear discrete boundary value problem of fractional order $1<\sigma<2$ with Riemann-Liouville fractional difference operator. Finally, some examples are presented to illustrate the main results.

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