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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 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.$$\left\{ {\matrix{ {AB{C_a}D_\tau ^\theta [x(\vartheta ) - F(\vartheta ,x(\vartheta ))] = G(\vartheta ,x(\vartheta )),\;\;\;{\kern 1pt} \vartheta \in J: = [a,b],} \hfill \cr {x(a) = {\varphi _a} \in .} \hfill \cr } } \right.$$

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 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.

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 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.

This paper deals with some existence and uniqueness results for a class of problems systems for nonlinear k$$ k $$‐generalized ψ$$ \psi $$‐Hilfer fractional differential equations with periodic conditions. The arguments are based on Mawhin's coincidence degree theory. Furthermore, an illustration is presented to demonstrate the plausibility of our results. [ABSTRACT FROM AUTHOR]

This manuscript is devoted to proving some results concerning the existence of solutions for a class of initial value problem for nonlinear implicit fractional Hybrid differential equations and improved conformable fractional derivative. The result is based on a fixed point theorem due to Dhage. Further, an example is provided for the justification of our main result. [ABSTRACT FROM AUTHOR]

In the present article, we prove some results concerning the existence of solutions for a class of initial value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer fractional derivative. The results are based on Banach contraction principle and Schaefer's fixed point theorem. Examples are included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this article, we present some results on the existence and uniqueness of random solutions to a non-linear implicit fractional differential equation involving the generalized Caputo fractional derivative operator and supplemented with non-local and periodic boundary conditions. We make use of the fixed point theorems due to Banach and Krasnoselskii to derive the desired results. Examples illustrating the obtained results are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and Ulam stability results for a class of boundary value problems for implicit Riesz-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The result are based on Monch fixed point theorem associated with the technique of measure of noncompactness. An illustrative example is given to validate our main results. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-metric spaces with initial and nonlocal conditions. The arguments are based on some fixed point theorems. Furthermore, two illustrations are presented to demonstrate the plausibility of our results. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the existence and uniqueness of periodic solutions for some class of nonlinear fractional pantograph systems with -Hilfer derivative. The proofs are based upon the coincidence degree theory of Mawhin. To show the efficiency of the stated result, an illustrative example will be demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, we present some results on existence and uniqueness for a class of boundary value problems for iterative fractional differential equations with generalized Caputo fractional derivative. For our proofs, we employ some suitable fixed point theorems. Finally, we provide an illustration for more clarity. [ABSTRACT FROM AUTHOR]

In this paper. we establish sufficient conditions for the existence of solutions for a class of nonlinear Hilfers fractional differential equations, The arguments are based upon the Banach contraction principle and Schaefers fixed point theorem. Two examples are included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence, uniqueness and stability results for a class of nonlinear impulsive Hilfer-Katugampola problems. Our reasoning is founded on the Banach contraction principle and Krasnoselskii's fixed point theorem. In addition, an example is provided to demonstrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and uniqueness of solutions to boundary value problem for differential equations with generalized Hilfer type fractional derivative. The arguments are based upon the Banach contraction principle and Krasnoselskii's fixed point theorem. An example is included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the existence and uniqueness of solutions of a coupled system of nonlinear implicit fractional differential equations of Caputo-type modification of the Erdélyi-Kober involving both retarded and advanced arguments. The arguments are based upon the Banach contraction principle and Schauder's fixed point theorem. An example is included to show the applicability of our outcomes. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the existence, uniqueness, Eα-Ulam stability results, and other properties of solutions for certain classes of nonlinear fractional differential equations involving the -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 Eα-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. [ABSTRACT FROM AUTHOR]

This paper deals with existence and uniqueness of solutions to a class of impulsive boundary value problem for nonlinear implicit fractional differential equations involving the Caputo-exponential fractional derivative. The existence results are based on Schaefer's fixed point theorem and the uniqueness result is established via Banach's contraction principle. Two examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

We provide some sufficient conditions ensuring the existence of solutions of Caputo type modification of the Erdélyi-Kober fractional differential inclusions in Banach spaces with retarded and advanced arguments. We use Mönch's and Darbo's fixed point theorems and the concept of a measure of noncompactness. As illustration, an example is presented. [ABSTRACT FROM AUTHOR]

This article deals with results concerning the existence of solutions for some functional implicit of Caputo type modification of the Erdélyi-Kober fractional differential equations, with both retarded and advanced arguments. The results are based on the Mönch's and Darbo's fixed point theorem associated with the technique of measure of noncompactness, and we present an illustrative example. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the existence of mild solutions of some impulsive evolution fractional functional differential equations with non-local conditions. The results are obtained by using the Banach contraction principle and Krasnoselski's fixed point theorem combined with the a-Resolvent family. An example is presented to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, by using the fixed point theory and the technique relying on the concept of measure of noncompactness in Fréchet spaces, we prove some existence and Ulam-Hyers-Rassias stability results for some Hilfer and Hilfer-Hadamard fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we establish suffcient conditions for the existence and stability of solutions for a class of nonlocal initial value problems for differential equations with Hilfer's fractional derivative, The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and uniqueness of solutions for a class of anti-periodic boundary value problem for nonlinear implicit fractional differential equations with impulse and Caputo fractional derivative. 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. [ABSTRACT FROM AUTHOR]

In this research paper, we present some results about the existence and uniqueness of periodic solutions for a great nonlinear class of Volterra-Fredholm integro-differential equations equipped with fractional integral conditions, involving ψ -Hilfer fractional operator. This investigation is carried out by means of the coincidence degree theory of Mawhin. A typical example is also presented. [ABSTRACT FROM AUTHOR]

This manuscript is concerned with the existence of solutions for a class of boundary value problems for nonlinear fractional hybrid differential equations involving generalized Hilfer fractional derivative. The main result is based on a fixed point theorem due to Dhage, which is illustrated with examples. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions for the existence of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. We apply the technique of measure of noncompactness and the fixed point theorems of Darbo and Mönch. As an application, two examples are included to show the applicability of our results. [ABSTRACT FROM AUTHOR]