In this paper, we study existence and approximation of solutions to some threepoint boundary value problems for fractional differential equations of the type Dq 0+u(t) + f(t, u(t)) = 0, t ∈ (0, 1), 1 < q < 2 u′(0) = 0, u(1) = ξu(η), where 0 < ξ, η ∈ (0, 1) and Dq 0+ is the fractional derivative in the sense of Caputo. For the existence of solution, we develop the method of upper and lower solut...

Fractional Galilei invariant advection–diffusion (GIADE) equation, along with its more general version that is the GIADE equation nonlinear source term, discretized by coupling weighted and shifted Grünwald difference approximation formulae Crank–Nicolson technique. The new of backward substitution method, a well-established class meshfree methods, proposed for numerical consequent equation. In...

In this paper, we developed a new variational iteration method using the quasilinearization and Adomian polynomial to solve nonlinear differential equations. The convergence analysis of our is also discussed under Lipschitz continuity condition in Banach space. Some application problems are included test efficacy proposed method. behavior investigated for different values parameter t. This powe...

and Applied Analysis 3 Table 1 Quasilinearization method Integer derivative Caputo’s derivative Monotone sequences Yes Yes Unique solution exists Yes Yes Uniform convergence Yes Yes Quadratic semiquadratic convergence Yes Yes Then, α0 ≤ β0 0, where α0 α0 t t − t0 |t t0 and β0 0 β0 t t − t0 |t t0 imply that α0 t ≤ β0 t , t0 ≤ t ≤ T. Corollary 2.2. The function F t, u σ t u, where σ t ≤ L, is adm...

The ultimate goal of this study is to develop a numerically effective approximation technique acquire numerical solutions the integer and fractional-order Bratu singular Lane–Emden-type problems especially with exponential nonlinearity. Both initial boundary conditions were considered fractional derivative being in Liouville–Caputo sense. In direct approach, generalized Bessel matrix method bas...

Data fusion techniques combine data from multiple sensors, and related information from associated databases, to achieve improved accuracies and more specific inferences than could be achieved by the use of a single sensor alone. This paper presents the fusion using the generalized quasilinearization technique to obtain a monotone sequence of iterates, converging uniformly for the tracks, obtai...

In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear di...

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of the proof to partial differential equations is straight forward. The method, whose mathematical basis in physics was discussed recently by one of the present ...