Related papers: Positive solutions of a nonlocal Caputo fractional…
In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential equation. We establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove…
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation \begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+\lambda…
In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. Using spectral expansion method, we give explicit forms of…
We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…
In this article, we establish the symmetric positive existence for the following Caputo fractional boundary value problem \begin{align*} {}^{C}D_{0}^{\,\mu}x(t)+f(t,x(t))&=0,\hspace{1cm}t\in(-1,\,1),\hspace{1cm}1<\mu\leq2,\\…
This paper deals with the initial value problem for the multi-term fractional differential equation. The fractional derivative is defined in the Caputo sense. Firstly the initial value problem is transformed into a equivalent Volterra-type…
This paper contain a new discussion for the type of generalized nonlinear Caputo fractional $q$-difference equations with $m$-point boundary value problem and Riemann-Stieltjes integral $\tilde{\alpha}[x]:=\int_{0}^{1}~x(t)d\Lambda(t).$ By…
In this paper, we investigate the existence and uniqueness of solution of nonlinear $\psi$-Caputo fractional differential equation with the help of Banach fixed point theorem. Moreover, by using $\psi$-Gronwall inequality, we studied some…
We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the the pseudo-index…
In the present work, we investigate a uniqueness of solution of the inverse source problem with non-local conditions for mixed parabolic-hyperbolic type equation with Caputo fractional derivative. Solution of the problem we represent as…
In the paper, we considered the existence and uniqueness of the global solution in the space of continuously differentiable functions for a nonlinear differential equation with the Caputo fractional derivative of general form. Our main…
We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions.
In this work we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic type equation with three lines of type-changing with Caputo fractional derivative in the parabolic part. We equivalently reduce…
We shall firstly study the existence of one positive solution of a model problem for one equation via the classical Krasnosel'ski\u\i{} fixed-point theorem. Secondly we investigate how to handle this problem via the fixed point index theory…
Using the theory of fixed point index, we discuss existence, non-existence, localization and multiplicity of positive solutions for a $(p_1,p_2)$-Laplacian system with nonlinear Robin and/or Dirichlet type boundary conditions. We give an…
In this article, we obtain existence and uniqueness results to some problems involving complex nonlinear fractional differential equations (FDEs) in the closed unit disc of C. By help of these results, we prove that some IVPs for some…
We provide new results on the existence of nonzero positive weak solutions for a class of second order elliptic systems. Our approach relies on a combined use of iterative techniques and classical fixed point index. Some examples are…
We provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of Hammerstein integral equations. Some of the criteria involve a comparison with the spectral radii of some…