This article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applie

      In this paper fractional Maxwell fluid equation has been solved. The solution is in the Mettag-Leffler form. For  the corresponding solutions for ordinary Maxwell fluid are obtained as limiting case of general solutions. Finally, the effects of different parameters on the velocity and shear stress profile are analyzed through plotting the velocity and shear stress profile.

Simulation of free convection heat transfer in a square enclosure induced by heated thin plate is represented numerically. All  the enclosure walls have constant temperature lower than the plate’s temperature. The flow is assumed to be two-dimensional. The discretized equations were solved stream function, vorticity, and energy equations by finite difference method using explicit technique and Successive Over- Relaxation method. The study was performed for different values of Rayleigh number ranging from 10³ to 10⁵ for different angle position of heated thin plate(0°, 45°, 90°). Air was chosen as a working fluid (Pr = 0.71). Aspect ratio of center of plate to the parallel left wall A₂

Classical cryptography systems exhibit major vulnerabilities because of the rapid development of quan tum computing algorithms and devices. These vulnerabilities were mitigated utilizing quantum key distribution (QKD), which is based on a quantum no-cloning algorithm that assures the safe generation and transmission of the encryption keys. A quantum computing platform, named Qiskit, was utilized by many recent researchers to analyze the security of several QKD protocols, such as BB84 and B92. In this paper, we demonstrate the simulation and implementation of a modified multistage QKD protocol by Qiskit. The simulation and implementation studies were based on the “local_qasm” simulator and the “FakeVigo” backend, respectively. T