65 Results Found

The method of the equivalent system of fractional integral equations is used to prove the existence results of a unique solution for initial value problems corresponding to various classes of nonlinear fractional differential equations involving the...

In this paper, the nonlinear version of the Henry–Gronwall integral inequality with the tempered $\Psi$-Hilfer fractional integral is proved. The particular cases, including the linear one and the nonlinear integral inequality of this type with...

The primary aim of this study is to establish new Wirtinger-type inequalities involving fractional derivatives, which are essential tools in analysis and applied mathematics. We derive generalized Wirtinger-type inequalities incorporating the $(k,\mathrm{\&psi}$...

In the current paper, we analyzed the existence and uniqueness of a solution for a coupled system of impulsive hybrid fractional differential equations involving $\psi$-Caputo fractional derivatives with generalized slit-strips-type integral boundary...

In this research work, we use the concepts of contraction mapping to establish the existence and uniqueness results and also study the averaging principle in ${\mathbb{L}}^p$ space by using Jensen’s, Grönwall–Bellman’s, Hölder’s,...

Recently, many scientists have studied a wide range of strategies for solving characteristic types of symmetric differential equations, including symmetric fractional differential equations (FDEs). In our manuscript, we obtained sufficient conditions...

In this work, we explore Wirtinger-type inequalities involving tempered Ψ-Caputo fractional derivatives by utilizing Taylor’s formula. We establish more general inequalities for the same operator in $L_p$ norms for $p>1$ by using Hölder&...

In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with $\psi$ -Riesz-Caputo fractional derivative. A new definition of $\psi$ -Riesz-Caputo fractional derivative of order...

In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the $\psi$ -Caputo derivative. Moreover, some uniqueness results are obtained. Our...

In this paper, we investigate a new class of nonlinear fractional integrodifferential systems that includes the $\Psi$-Riemann–Liouville fractional integral term. Using the technique of upper and lower solutions, the solvability of the system is...

In this paper, the tempered $\mathsf{\Psi }$–Riemann–Liouville fractional derivative and the tempered $\mathsf{\Psi }$–Caputo fractional derivative of order $n-1<\alpha <n\in \mathbb{N}$ are introduced for $C^{n-1}$–functions. A nonlinear versi...

The current study is devoted to investigating the existence and uniqueness of solutions for a new class of symmetrically coupled system of nonlinear hyperbolic partial-fractional differential equations in generalized Banach spaces in the sense of $\mathrm{\&ps}$...

In this article, we investigate the existence of solutions for a class of fractional integro-differential equations (FIDE’s) involving the $\psi$-Caputo fractional derivative ($\psi$-CFD) subject to $\psi$-Caputo boundary conditions. The analysis...

The objective of this paper is to study the existence of extremal solutions for nonlinear boundary value problems of fractional differential equations involving the $\mathsf{\psi }-$Caputo derivative ${}^C{\mathbb{D}}_{a^{+}}^{\sigma ;\mathsf{\psi }}\varrho \left(\mathrm{t}\right)=\mathcal{V}(\mathrm{t},\varrho \left(\mathrm{t}\right))$ under integral boundary conditions $\varrho \left(a\right)=\lambda {\mathbb{I}}^{\nu }$...

A novel fixed-point theorem based on the degree of nondensifiability (DND) is used in this article to examine the existence of solutions to a boundary value problem containing the $\psi$-Caputo fractional derivative in Banach spaces. Besides that, an...

The primary objective of this study is to investigate the concept of approximate controllability in fractional evolution equations that involve the ψ-Caputo derivative. Specifically, we examine the scenario where the semigroup is compact and anal...

In this paper, the existence of a unique solution is established for a coupled system of Langevin fractional problems of $\mathsf{\psi }$-Caputo fractional derivatives with generalized slit-strip-type integral boundary conditions and impulses using the Banach c...

This manuscript, we establish novel findings regarding the existence of solutions for second-order fractional differential equations employing $\Psi$-Caputo fractional derivatives. The application of Banach’s fixed-point theorem (BFPT) ensures t...

Closed-form Caputo gradients in critical-state stress-fractional plasticity have relied on the polynomial Modified Cam-Clay surface. We extend them to the non-polynomial teardrop bounding surface by defining the operator as a Caputo derivative in the...

This study investigates fuzzy fixed points and fuzzy best proximity points for fuzzy mappings within the newly introduced framework $\theta$-fuzzy metric spaces that extends various existing fuzzy metric spaces. We establish novel fixed-point and best...

We establish sufficient conditions for the existence and exponential stability of mild solutions of a class of fractional neutral stochastic integro-differential delay systems governed by the $\psi$-Caputo fractional derivative of order $\sigma \in ($...

In this paper, we introduce and study a new class of coupled and uncoupled systems, consisting of mixed-type ${\psi }_1$-Hilfer and ${\psi }_2$-Caputo fractional differential equations supplemented with asymmetric and symmetric integro-differential nonlocal bo...

An initial value problem for nonlinear fractional differential equations with a tempered Caputo fractional derivative of variable order with respect to another function is studied. The absence of semigroup properties of the considered variable order...

We study a boundary value problem for a $(k,\psi )$-Hilfer–Caputo fractional neutral differential equation supplemented with multi-point and multi-strip non-local boundary conditions. An equivalent integral formulation is first derived via an aux...

This paper investigates the existence and uniqueness of solutions to a class of sequential fractional differential equations and inclusions involving the $(k,\psi )$-Hilfer and $(k,\psi )$-Caputo derivatives under non-separated boundary conditions. By re...

This paper investigates the absence of globally defined, non-trivial solutions for some fractional differential inequalities of the $\psi$-Caputo type, with polynomial sources involving fractional derivatives. We rigorously establish these results wit...

An initial boundary value problem for a fractional in time and space shallow-water system involving $\psi$ -Caputo fractional derivatives of different orders is considered. Using the test function method, sufficient criteria for the absence of gl...

This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized $\psi$-Caputo fractional derivative with a weight. Depending on critical point theorems and some properties of $\psi$-Caput...

This paper investigates a coupled system of nonlinear implicit fractional differential equations of order $\alpha \in (1,2]$ subject to anti-periodic boundary conditions. The analysis is conducted using the $\psi$-Caputo fractional derivative, a gener...

In this article, we investigate sufficient conditions for the existence and stability of solutions to a coupled system of $\psi$-Caputo hybrid fractional derivatives of order $1<\upsilon \le 2$ subjected to Dirichlet boundary conditions. We discuss t...

This paper investigates a new class of mixed impulsive fractional boundary value problems (BVPs) in which the mixing occurs both in the governing fractional differential equations—through the combined presence of $\psi$-Caputo and quantum (q-dif...

In this research work, we investigate a nonlinear fractional initial value problem involving the Atangana-Baleanu-Caputo derivative of order $0<\alpha <1.$ By means of the associated fractional integral operator, the problem is converted into an...

This article aims to explore the existence and stability of solutions to differential equations involving a $\psi$-Hilfer fractional derivative in the Caputo sense, which, compared to classical $\psi$-Hilfer fractional derivatives (in the Riemann&ndash...

In this paper, we investigate a new class of nonlinear fractional boundary value problems (BVPs) involving $(k,\psi )$-Caputo fractional derivative operators subject to multipoint closed boundary conditions. Such a formulation of boundary data generali...

This paper considers a nonlinear impulsive fractional boundary value problem, which involves a $\psi$-Caputo-type fractional derivative and integral. Combining critical point theory and fractional calculus properties, such as the semigroup laws, and r...

In this study, we introduced the $\psi$-Laplace transform Adomian decomposition method, which is a combination of the efficient Adomian decomposition method with the generalization of the classical Laplace transform to treat fractional differential eq...

The aim of this work is to analyze the relative controllability and Ulamn–Hyers stability of the $\mathsf{\psi }$-Caputo fractional neutral delay differential system. We use neutral $\mathsf{\psi }$-delayed perturbation of the Mitttag–Leffler matrix...

In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit $\psi$-Caputo fractional differential equations with non-instantaneous impulses involving both retarde...

This paper is concerned with the existence and uniqueness of solutions for a coupled system of $(k,\psi )$-Hilfer and $(k,\psi )$-Caputo sequential fractional differential equations with non-separated boundary conditions. We make use of the Banach contra...

In this paper, the existence and uniqueness of solutions for a coupled system of ψ-Hilfer type sequential fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions is investigated. The presented results are...

In this paper we study single-valued and multi-valued (k,ψ)-Hilfer-type boundary value problems of fractional order in (1,2], subject to nonlocal boundary conditions involving (k,ψ)-Hilfer-type derivative and integral operators. The results f...

In this paper, we establish existence and uniqueness results for single-valued as well as multi-valued $(k,\psi )$-Hilfer boundary value problems of order in $(1,2],$ subject to nonlocal integro-multi-point boundary conditions. In the single-valued case,...

In this paper, we introduce and study a new class of boundary value problems, consisting of a mixed-type ${\psi }_1$-Hilfer and ${\psi }_2$-Caputo fractional order differential equation supplemented with integro-differential nonlocal boundary conditions. The u...

In this article, by combining a recent critical point theorem and several theories of the ψ-Caputo fractional operator, the multiplicity results of at least three distinct weak solutions are obtained for a new ψ-Caputo-type fractional differe...

The existence of mild solutions and the approximate controllability for a class of Sobolev-type $\psi$-Caputo fractional stochastic evolution equations (SCFSEEs) subject to nonlocal conditions and Poisson jumps are investigated in this paper. First, t...

This paper is devoted to the study of existence and uniqueness of solutions for fractional functional differential equations, whose derivative operator depends on an arbitrary function. The introduction of such function allows generalization of some...

In this paper, we investigate the controllability of a class of impulsive $\psi$-Caputo fractional evolution equations of Sobolev type in Banach spaces. Sufficient conditions are presented by two new characteristic solution operators, fractional calcu...

This paper is dedicated to the discussion of a new long memory $\psi$-Caputo fractional viscoelastic friction contact problem with adhesion in symmetric dual spaces. In this contact model, the contact condition is described by Clarke-generalized gradi...

Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving $\alpha$-$\psi$-con...

This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety of fractional derivative operators and boundary conditions. Our work deals with Caputo, Riema...