In this paper, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...

This paper develops a two-level fourth-order scheme for solving time-fractional convection–diffusion–reaction equation with variable coefficients subjects to suitable initial and boundary conditions. The basis properties of the new approach are investigated both stability error estimates proposed numerical deeply analyzed in L∞(0,T;L2)-norm. theory indicates that method is unconditionally stabl...

Abstract The fractional model has been developed for the thermal flow of hybrid nanofluid due to inclined surface. investigation nanomaterial is predicted by utilizing molybdenum disulphide nanoparticles and graphene oxide nanomaterials. computations mixed convection base fluids are performed vertical oscillating plate. simulations formulated have done ρ -Laplace transform technique Caputo simu...

In this paper, we study the numerical solution to time-fractional partial differential equations with variable coefficients that involve temporal Caputo derivative. A spectral method based on Gegenbauer polynomials is taken for approximating the solution of the given time-fractional partial differential equation in time and a collocation method in space. The suggested method reduces this type o...

The source terms of the Baer–Nunziato model involve highly non-linear return to equilibrium terms. In order perform numerical simulations realistic situations, accounting for this relaxation effects is mandatory. Unfortunately, with classical forms retained these in literature, building efficient, robust and accurate schemes a tricky task. paper, we propose different non-classical As ones, they...

where is a bounded region with piecewise smooth boundary . R    is a small positive constant and is a smooth vector function on   u f   F x x  1 2 u        3 f u f u    x x  R  ,   0 0   F x . The finite volume element method (FVEM) is a discrete technique for partial differential equations, especially for those arising from physical conservation laws, including mass,...

effects of formulation parameters on the fractional release profile of diclofenac sodium from matrices having the manufacturing formulation ingredients are studied. as a content of cetyl alcohol (rate controlling agent) in the matrix increases, the fractional release decreases. the fractional release increases either by increasing sucrose content outside the granule or by decreasing sucrose con...

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...