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The main goal of this article is to study the existence and uniqueness of periodic solutions for the implicit problem with nonlinear fractional differential equation involving the Caputo tempered fractional derivative. The proofs are based upon the coincidence degree theory of Mawhin. To show the efficiency of the stated result, two illustrative examples will be demonstrated.

In this article, we study the existence of mild solutions of a non-instantaneous integrodi erential equations on unbounded domain via resolvent operators in Banach space. For our proofs, we employ the semigroups theory and Schauder’s fixed point theorem. Moreover, we show that solutions of our problem are attractive. Finally, an example is given to validate the theory part.

This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach spaces. We prove a theorem on the global convergence of successive approximations to the unique solution of the problems. An example is given to show the application of our result.

The aim of this paper is to study the existence of the unique mild solution for non-linear fractional integro-differential equations with state-dependent nonlocal condition. The result was obtained by using nonlinear alternative of Granas-Frigon for contraction in Fréchet spaces. To illustrate the result, an example is provided.

In this paper, we study the following fractional differential equation involving the Atangana-Baleanu-Caputo fractional derivative: {ABCaDτθ[x(ϑ)−F(ϑ,x(ϑ))]=G(ϑ,x(ϑ)), ϑ∈J:=[a,b],x(a)=φa∈ℝ.$$\left\{ {\matrix{ {AB{C_a}D_\tau ^\theta [x(\vartheta ) - F(\vartheta ,x(\vartheta ))] = G(\vartheta ,x(\vartheta )),\;\;\;{\kern 1pt} \vartheta \in J: = [a,b],} \hfill \cr {x(a) = {\varphi _a} \in .} \hfill \cr } } \right.$$

This paper deals with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-Metric spaces with initial nonlocal conditions and instantaneous impulses. The results are based on the o - d-Geraghty type contraction, the F-contraction and the fixed point theory. Furthermore, some illustrations are presented to demonstrate the plausibility of our results.

In this paper, we establish the existence of solutions for a class of nonlinear implicit neutral fractional differential equations with terminal condition and Hilfer-Katugampola fractional derivative. The Banach contraction principle and Krasnoselskii’s fixed point theorem are used to support the arguments. An illustration is provided to demonstrate the relevance of our results.

In this manuscript, by using weakly Picard operators we investigate the Ulam type stability of fractional q-difference An illustrative example is given in the last section.

We deal with some impulsive Caputo-Fabrizio fractional differential equations in bb-metric spaces. We make use of α-ϕ\alpha \text{-}\phi -Geraghty-type contraction. An illustrative example is the subject of the last section.

In this paper, we prove some existence results of solutions for a class of nonlocal initial value problem for nonlinear fractional hybrid implicit differential equations under generalized Hilfer fractional derivative. The result is based on a fixed point theorem on Banach algebras. Further, examples are provided to illustrate our results.

The main purpose of this paper is to study the existence, uniqueness, Ea-Ulam stability results, and other properties of solutions for certain classes of nonlinear fractional differential equations involving the ps-Caputo derivative with initial conditions. Modern tools of functional analysis are applied to obtain the main results. More precisely using Weissinger's fixed point theorem and Schaefer's fixed point theorem the existence and uniqueness results of solutions are proven in the bounded domain. While the well known Banach fixed point theorem coupled with Bielecki type norm are used with the end goal to establish sufficient conditions for existence and uniqueness results on unbounded domains. Meanwhile, the monotone iterative technique combined with the method of upper and lower solutions is used to prove the existence and uniqueness of extremal solutions. Furthermore, by means of new generalizations of Gronwall's inequality, different kinds of Ea-Ulam stability of the proposed problem are studied. Finally, as applications of the theoretical results, some examples are given to illustrate the feasibility and correctness of the main results.

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.

In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.

In this paper, we use some background concerning multivalued functions and set-valued analysis, the fixed point theorem of Bohnenblust-Karlin and the method of upper and lower solutions to investigate the existence of solutions for a class of boundary value problem of functional differential inclusions involving the Caputo-Hadamard fractional derivative.

In this paper, we prove the existence of mild solution for impulsive fractional inclusions with state-dependent delay in Banach spaces. Our study is based on the nonlinear alternative of Leray-Schauder type for multivalued maps due to Martelli. An example is provided to illustrate the main result.

In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Hadamard fractional order. We use an extension of the Burton-Kirk fixed point theorem in Fréchet spaces.

In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.

In the present paper we provide some existence results for the Darboux problem of partial fractional random differential equations with state-dependent delay by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.

In this paper, we establish sufficient conditions for the existence and stability of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results.

In this article, we investigate some Ulam’s type stability concepts for the Darboux problem of partial fractional differential inclusions with a nonconvex valued right hand side. Our results are based upon Covitz-Nadler fixed point theorem and fractional version of Gronwall’s inequality.

In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.

The nonlinear alternative of the Leray Schauder type and the Banach contraction principle are used to investigate the existence of solutions for second-order differential equations with integral boundary conditions. The compactness of solutions set is also investigated.

Abstract We investigate the global existence and uniqueness of solutions for some classes of partial hyperbolic differential equations involving the Caputo fractional derivative with finite and infinite delays. The existence results are obtained by applying some suitable fixed point theorems.

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

We establish sufficient conditions for the existence of mild solutions for some densely defined semilinear functional differential equations and inclusions involving the Riemann-Liouville fractional derivative. Our approach is based on the -semigroups theory combined with some suitable fixed point theorems.

We discuss the existence of oscillatory and nonoscillatory solutions for first-order impulsive dynamic equations on time scales with certain restrictions on the points of impulse. We will rely on the nonlinear alternative of Leray-Schauder type combined with a lower and upper solutions method.