Fractional Differential Equations

We investigate a coupled system of fractional differential equations with nonlinearities depending on the unknown functions as well as their lower order fractional derivatives supplemented with coupled nonlocal and integral boundary conditions. We emphasize that the problem considered in the present setting is new and provides further insight into the study of nonlocal nonlinear coupled boundary value problems. We present two results in this paper: the first one dealing with the uniqueness of solutions for the given problem is established by applying contraction mapping principle, while the second one concerning the existence of solutions is obtained via Leray–Schauder’s alternative. The main results are well illustrated with the aid of examples.

On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions

We study a nonlocal boundary value problem of Hadamard type coupled sequential fractional differential equations supplemented with coupled strip conditions (nonlocal Riemann-Liouville integral boundary conditions). The nonlinearities in the coupled system of equations depend on the unknown functions as well as their lower order fractional derivatives. We apply Leray-Schauder alternative and Banach’s contraction mapping principle to obtain the existence and uniqueness results for the given problem. An illustrative example is also discussed.

A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions

Abstract We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations, subject to coupled integral boundary conditions. The nonsingular and singular cases are studied.

On a System of Fractional Differential Equations with Coupled Integral Boundary Conditions

We investigate the nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions.

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Nonexistence of positive solutions for a system of coupled fractional boundary value problems

We study the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to integral boundary conditions. MSC:34A08, 45G15.

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Positive solutions to a system of semipositone fractional boundary value problems

We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.

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Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

We study the existence and nonexistence of positive solutions for a system of Riemann–Liouville fractional differential equations with p-Laplacian operators, nonnegative nonlinearities and positive parameters, subject to coupled nonlocal boundary conditions which contain Riemann–Stieltjes integrals and various fractional derivatives. We use the Guo–Krasnosel’skii fixed point theorem in the proof of the main existence results.

/pdf/positive-solutions-for-a-system-of-riemann-liouville-4snibcm8l9.pdf

Positive solutions for a system of Riemann–Liouville fractional boundary value problems with p-Laplacian operators

We study the existence and multiplicity of positive solutions fora system of nonlinear second-order digerence equations sub ject to multi-pointboundary conditions

/pdf/multiple-positive-solutions-for-a-multi-point-discrete-3br091ji3n.pdf

Alexandru Tudorache

Papers

On a System of Fractional Differential Equations with Coupled Integral Boundary Conditions

Positive solutions to a system of semipositone fractional boundary value problems

Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

Positive solutions for a system of Riemann–Liouville fractional boundary value problems with p-Laplacian operators

Multiple positive solutions for a multi-point discrete boundary value problem