Existence results for nonlinear Hilfer and Caputo fractional differential equations with separated boundary conditions in Banach spaces

This paper is devoted to the existence of solutions for certain classes of nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with Dirichlet boundary conditions in Banach spaces. Moreover, our analysis is based on Darbo’s fixed point theorem in conjunction with the technique of Hausdorff measure of noncompactness. An example is also presented to illustrate the effectiveness of the main results.

This paper deals with nonlinear fractional differential equation with fractional separated boundary conditions. We investigate the existence of weak solutions in Banach spaces. To obtain such result we apply an appropriate fixed point theorem and the technique of measures of weak noncompactness. An example illustrating the theory is given.

Positive solutions of [formula omitted]th-order impulsive boundary value problems with integral boundary conditions in Banach spaces

The nonlinear fractional differential equation with nonlocal fractional integro-differential boundary conditions in Banach spaces is studied, an existence result is obtained by using the method associated with the technique of measures of noncompactness and an appropriate fixed point theorem. An example is given to illustrate the theory.

Positive solutions to fourth-order singular boundary value problems with integral boundary conditions in abstract spaces

By means of the fixed point theory for a strict set contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a nonlinear higher order boundary value problem with four point fractional integral boundary conditions in Banach spaces. In addition, an example is worked out to illustrate the main results.

The main purpose of this paper is to provide the theory of differential inclu- sions by new existence results of solutions for boundary value problems of differential inclusions with fractional order and with anti-periodic boundary conditions in Banach spaces. We prove existence theorems of solutions under both convexity and nonconvex- ity conditions on the multivalued side. Meanwhile, the compactness of the set solutions is also established.

In this paper, we study the existence of solutions for nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with three-point boundary conditions by using measure of noncompactness combined with fixed point theorem of M?nch. An example illustrating the effectiveness of the theoretical results is presented.

Generalized boundary value problems (BVP) typically cover a wide range of equations. In this study, we focus on a generalization of Caputo-type fractional discrete differential equations that involve two or more fractional q-integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVP based on several fixed point theorems, including the Banach fixed point theorem, the nonlinear Leray-Schauder alternative, and the Leray-Schauder degree theory. Finally, several examples are presented to illustrate the accuracy of our results.

This paper is devoted to the existence of weak solutions for a multipoint fractional integral boundary value problem of an impulsive nonlinear differential equation involving multiorders fractional derivatives and deviating argument. We make use of an appropriate fixed point theorem combined with the technique of measures of weak noncompactness. Our investigation is considered in a Banach space. The applicability of the obtained results is illustrated by an example.

This paper investigates the existence results and uniqueness of solutions for a class of boundary value problems for fractional differential equations with the Hilfer fractional derivative. The reasoning is mainly based upon Mönch’s fixed point theorem associated with the technique of measure of noncompactness. We illustrate our main findings, with a particular case example, included to show the applicability of our outcomes. The boundary conditions introduced in this work are of quite general nature and reduce to many special cases by fixing the parameters involved in the conditions.

The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.

Fractional p-Laplacian differential equations with multi-point boundary conditions in Banach spaces

This article deals with some existence of random solutions and Ulam stability results for a class of Caputo-Fabrizio random fractional differential equations with boundary conditions in Banach spaces. Our results are based on the fixed point theory and random operators. Two illustrative examples are presented in the last section.

Positive solutions for a class of boundary-value problem with integral boundary conditions in Banach spaces