The convergence analysis and error estimation for unique solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity

© 2018, The Author(s). In this paper, we focus on the convergence analysis and error estimation for the unique solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity. By introducing a double iterative technique, in the case of the nonlinearity with singularity at time and space variables, the unique positive solution to the problem is established. Then, from the developed iterative technique, the sequences converging uniformly to the unique solution are formulated, and the estimates of the error and the convergence rate are derived

Iterative algorithm and estimation of solution for a fractional order differential equation

In this paper, we establish an iterative algorithm and estimation of solutions for a fractional turbulent flow model in a porous medium under a suitable growth condition. Our main tool is the monotone iterative technique

Nonlocal q-fractional boundary value problem with Stieltjes integral conditions

In this paper, we are dedicated to investigating a new class of one-dimensional lower-order fractional q-differential equations involving integral boundary conditions supplemented with Stieltjes integral. This condition is more general as it contains an arbitrary order derivative. It should be pointed out that the problem discussed in the current setting provides further insight into the research on nonlocal and integral boundary value problems. We first give the Green's functions of the boundary value problem and then develop some properties of the Green's functions that are conductive to our main results. Our main aim is to present two results: one considering the uniqueness of nontrivial solutions is given by virtue of contraction mapping principle associated with properties of u0-positive linear operator in which Lipschitz constant is associated with the first eigenvalue corresponding to related linear operator, while the other one aims to obtain the existence of multiple positive solutions under some appropriate conditions via standard fixed point theorems due to Krasnoselskii and Leggett–Williams. Finally, we give an example to illustrate the main results. &nbsp

Twin iterative solutions for a fractional differential turbulent flow model

We investigate the existence of twin iterative solutions for a fractional p-Laplacian equation with nonlocal boundary conditions. Using the monotone iterative technique, we establish a new existence result on the maximal and minimal solutions under suitable nonlinear growth conditions. We also consider some interesting particular cases and give an example to illustrate our main results

Positive solution of singular fractional differential system with nonlocal boundary conditions

In this paper, we consider the existence of positive solutions for a singular fractionaldifferential system involving a nonlocal boundary condition which is given by a linearfunctional on C[0, 1] with a signed measure. By looking for the upper and lowersolutions of the system, the sufficient condition of the existence of positive solutionsis established; some further cases are discussed. This is proved in the case of strongsingularity and with a signed measure

Iterative positive solutions for singular nonlinear fractional differential equation with integral boundary conditions

In this article, we study the existence of iterative positive solutions for a class of singular nonlinear fractional differential equations with Riemann-Stieltjes integral boundary conditions, where the nonlinear term may be singular both for time and space variables. By using the properties of the Green function and the fixed point theorem of mixed monotone operators in cones we obtain some results on the existence and uniqueness of positive solutions. We also construct successively some sequences for approximating the unique solution. Our results include the multipoint boundary problems and integral boundary problems as special cases, and we also extend and improve many known results including singular and non-singular cases

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder’s fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables

On a Hadamard-type fractional turbulent flow model with deviating arguments in a porous medium

In this paper, we concern a Hadamard-type fractional-order turbulent flow model with deviating arguments. By using some standard fixed point theorems, the uniqueness, existence and nonexistence of solutions of the fractional turbulent flow model are investigated. Our results are new and are well illustrated with the aid of three examples

A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.&nbsp