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All over the world, people are facing the challenge of HIV as it affects the person suffering from it, the communities and the economy of society also. A lot of work has been done on different aspects of this dangerous disease by many researchers. Our task in this work is to lighten the ignorant aspect of this disease and to provide a continuous future prediction for the spread of this virus on a larger domain. For this purpose, a modification has been done in the mathematical model of HIV C D 4 + T -cells. And a semi-analytical technique has been applied on the system of nonlinear differential equations, governing the human immunodeficiency virus i-e HIV infection, of C D 4 + T -cells, to get convergent and continuous solutions. Graphical results and residual error for the solution of the nonlinear system of differential equations are also given. [ABSTRACT FROM AUTHOR]

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs. [ABSTRACT FROM AUTHOR]