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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.

In this paper, we establish sufficient criteria for ensuring the existence of solutions and uniqueness for a class of nonlinear neutral Caputo fractional differential equations supplemented with infinite delay and nonlocal boundary conditions involving fractional derivatives. The theory of infinite delay and standard fixed point theorems are employed to obtain the existence results for the given problem. Examples will be constructed to illustrate the obtained 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]

This article is devoted to showing the existence and uniqueness (EU) of a solution with non-Lipschitz coefficients (NLC) of fractional Itô-Doob stochastic differential equations driven by countably many Brownian motions (FIDSDECBMs) of order ϰ ∈ (0 , 1) by using the Picard iteration technique (PIT) and the semimartingale local time (SLT). [ABSTRACT FROM AUTHOR]

Abstract In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray–Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability of our results.

This article is devoted to showing the existence and uniqueness (EU) of a solution with non-Lipschitz coefficients (NLC) of fractional Itô-Doob stochastic differential equations driven by countably many Brownian motions (FIDSDECBMs) of order ϰ∈(0,1) by using the Picard iteration technique (PIT) and the semimartingale local time (SLT).

This manuscript is devoted to proving the existence of solutions to a class of initial value problems for nonlinear fractional Hybrid implicit differential equations with a ψ -Hilfer fractional derivative. The result is based on a fixed point theorem due to Dhage. Examples are provided to demonstrate the result. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence and uniqueness of solutions for a new kind of Langevin equation involving Riemann-Liouville as well as Caputo fractional derivatives, and variable coefficient, supplemented with nonlocal-terminal fractional integro-differential conditions. The proposed study is based on modern tools of functional analysis. We also extend our discussion to the associated inclusions problem. For the applicability of the obtained results, several examples are constructed. Some interesting observations are also presented.

In this paper, we introduce a new kind of generalized fractional integral boundary conditions and develop the existence theory for a fractional di erential equation involving generalized Caputotype fractional derivative equipped with these conditions. We also study the inclusion case of the given problem. Examples are constructed to demonstrate the application of the obtained results.

In this work, we discuss the existence of solutions for a coupled system of nonlinear fractional differential equations involving two Riemann-Liouville fractional orders. By applying the Leray-Schauder's nonlinear alternative and Banach's fixed-point theorem the existence and uniqueness of solutions is obtained. [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]

In this article, we obtain an existence result for periodic solutions to nonlinear implicit fractional differential equations with Caputo fractional derivatives. Our main tools is coincidence degree theory, which was first introduced by Mawhin. Also we present two examples to show the applicability of our results.

In this paper, we study the existence of solutions for a new nonlocal boundary value problem of integro-differential equations involving mixed left and right Caputo and Riemann−Liouville fractional derivatives and Riemann−Liouville fractional integrals of different orders. Our results rely on the standard tools of functional analysis. Examples are constructed to demonstrate the application of the derived 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.

In this paper, we establish the existence and uniqueness of solutions for a class of problem for nonlinear implicit fractional diffierential equations (NIFDE for short) of Hadamard type involving both retarded and advanced arguments. The proofs of our main results are based upon the Banach contraction principle and the Schauder fixed point theorem. We present two examples 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 paper, we establish the existence and uniqueness of solution for a class of initial value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder' fixed point theorem and the nonlinear alternative of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.

In this paper, we establish the existence and uniqueness of solution for a class of boundary value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder's fixed point theorem and the nonlinear alterna- tive of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.

In this paper, an existence result for a random fractional differential equation is established under a Carathéodory condition. Existence results for extremal random solutions are also proved. Finally, an existence and uniqueness result is given

We establish sufficient conditions for the existence of solutions for a nonlinear impulsive multi-order Caputo-type generalized fractional differential equation with infinite delay and nonlocal generalized integro-initial value conditions. The existence result is proved by means of Krasnoselskii’s fixed point theorem, while the contraction mapping principle is employed to obtain the uniqueness of solutions for the problem at hand. The paper concludes with illustrative examples.

We establish sufficient criteria for the existence of solutions for a nonlinear generalized Langevin-type nonlocal fractional-order integral multivalued problem. The convex and non-convex cases for the multivalued map involved in the given problem are considered. Our results rely on Leray−Schauder nonlinear alternative for multivalued maps and Covitz and Nadler’s fixed point theorem. Illustrative examples for the main results are included.

In this paper, we discuss the existence and uniqueness of solutions for a new class of single and multi-valued boundary value problems involving both Riemann–Liouville and Caputo fractional derivatives, and nonlocal fractional integro-differential boundary conditions. Our results rely on modern tools of functional analysis. We also demonstrate the application of the obtained results with the aid of examples.

In this paper, we investigate the existence of solution for boundary value problem with fractional differential equations with nonlocal conditions involving the standard Riemann-Liouville fractional derivative of order r ∈ (1; 2]. [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]

The purpose of this paper is to establish some types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of implicit Hadamard fractional-order differential equation. [ABSTRACT FROM AUTHOR]

In this article, we obtain an existence result for periodic solutions to nonlinear implicit fractional differential equations with Caputo fractional derivatives. Our main tools is coincidence degree theory, which was first introduced by Mawhin. Also we present two examples to show the applicability of our results. [ABSTRACT FROM AUTHOR]

We develop the existence criteria for solutions of Liouville⁻Caputo-type generalized fractional differential equations and inclusions equipped with nonlocal generalized fractional integral and multipoint boundary conditions. Modern techniques of functional analysis are employed to derive the main results. Examples illustrating the main results are also presented. It is imperative to mention that our results correspond to the ones for a symmetric second-order nonlocal multipoint integral boundary value problem under suitable conditions (see the last section).

We establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values. The topological structure of the set of solutions is also considered.

In this article, the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential inclusions involving the Caputo fractional derivative and nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered. The topological structure of the set of solutions also examined.

In this paper we study the existence of solutions for the initial value problem for semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Leray-Schauder type is the main tool in our analysis.

In this paper, we shall establish sufficient conditions for the existence of solutions for a first order boundary value problem for fractional differential equations.

In this paper, we investigate the existence of solutions for nonlocal boundary value problems for Riemann-Liouville fractional differential inclusions of order $${\alpha\in (1,2]}$$ . [ABSTRACT FROM AUTHOR]

In this paper, an existence result for a random fractional differential equation is established under a Carathéodory condition. Existence results for extremal random solutions are also proved. Finally, an existence and uniqueness result is given. [ABSTRACT FROM AUTHOR]

In this article, the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential inclusions involving the Caputo fractional derivative and nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered. The topological structure of the set of solutions also examined. [ABSTRACT FROM AUTHOR]

We establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values. The topological structure of the set of solutions is also considered. [ABSTRACT FROM AUTHOR]

In this survey paper, we shall establish sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problem for fractional differential equations and inclusions involving the Caputo fractional derivative. The both cases of convex and nonconvex valued right hand side are considered. The topological structure of the set of solutions is also considered. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential equations with variable times involving the Caputo fractional derivative. [Copyright &y& Elsevier]

Abstract: In this paper, we establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative and nonlocal conditions. [Copyright &y& Elsevier]

In this paper we study the existence of solutions for the initial value problem for semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Leray-Schauder type is the main tool in our analysis. [ABSTRACT FROM AUTHOR]

We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions, defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. [ABSTRACT FROM AUTHOR]

In this article, the authors establish sufficient conditions for the existence of solutions to a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative of order α ∈ (1, 2] and non-linear integral conditions. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish sufficient conditions for the existence of solutions for a first order boundary value problem for fractional differential equations [ABSTRACT FROM AUTHOR]

Abstract: The Banach fixed point theorem and the nonlinear alternative of Leray–Schauder type are used to investigate the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay. [Copyright &y& Elsevier]