In 1923, Hadamard encountered a class of integrals with strong singularities when using a particular Green’s function to solve the cylindrical wave equation. He ignored the infinite parts of such integrals after integrating by parts. Such an id...
This article investigates fractional Hermite–Hadamard integral inequalities through the framework of Caputo fractional derivatives and MET-(p,s)-convex functions. In particular, we introduce new modifications to two classical fractional extensi...
For analytic functions fj(z)=∑n=0∞an,jzn, 1≤j≤p, the notion of a Hadamard composition (f1∗…∗fp)m=∑n=0∞∑k1+⋯+kp=mck1…kpan,1k1·…·an,pkpzn of genus m is introduced. The...
The main aim of this paper is to investigate the combination synchronization phenomena of various fractional-order systems using the scaling matrix. For this purpose, the combination synchronization is performed by considering two drive systems and o...
In this paper, we study the existence and uniqueness of solutions for the following fractional boundary value problem, consisting of the Hadamard fractional derivative: HDαx(t)=Af(t,x(t))+∑i=1kCiHIβigi(t,x(t)),t∈(1,e), supplemente...
We prove the existence of solutions for neutral functional differential inclusions involving Hadamard fractional derivatives by applying several fixed point theorems for multivalued maps. We also construct examples for illustrating the obtained results.
This paper investigates the existence, uniqueness, and finite-time stability of solutions to a class of nonlinear systems governed by the Hadamard fractional derivative. The analysis is carried out using two fundamental tools from fixed point theory:...
By leveraging the concept of k-Caputo fractional derivatives for stochastic processes, in this paper, we derive a generalized Hermite–Hadamard inequality tailored to n-times differentiable convex stochastic processes, providing a powerful tool...
In this study, we focus on the stability analysis of the RLC model by employing differential equations with Hadamard fractional derivatives. We prove the existence and uniqueness of solutions using Banach’s contraction principle and Schaefer&rs...
This study investigates the absence of global solutions for a system of fractional differential equations. The system features a nonlinear source term with nonlocal temporal behavior and involves two Hadamard fractional derivatives (HFDs) of varying...
In this paper, a rigorous Lyapunov direct method (LDM) is proposed to analyze the stability of fractional non-linear systems involving Hadamard or Caputo–Hadamard derivatives. Based on the characteristics of Hadamard-type calculus, several new...
The authors obtain existence and uniqueness results for a nonlinear fractional pantograph boundary value problem containing a variable order Hadamard fractional derivative. This type of model is appropriate for applications involving processes that o...
This paper discusses the problem of the existence and uniqueness of solutions to the boundary value problem for the nonlinear fractional-order pantograph equation, using the fractional derivative of variable order of Hadamard type. The main results a...
In this paper, we study the Caputo–Hadamard time-space fractional diffusion equation, where the Caputo derivative is defined in the temporal direction and the Hadamard derivative is defined in the spatial direction separately. We first use the...
In this paper, we study a coupled system of Caputo-Hadamard type sequential fractional differential equations supplemented with nonlocal boundary conditions involving Hadamard fractional integrals. The sufficient criteria ensuring the existence and u...
In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing the classical time derivative with the...
A general fractional scale derivative is introduced and studied. Its relation with the Hadamard derivatives is established and reformulated. A new derivative similar to the Grünwald–Letnikov’s is deduced. Tempered versions are also i...
This paper presents an extensive investigation into the state feedback stabilization, observer design, and observer-based controller design for a specific category of nonlinear Hadamard fractional-order systems. The research extends the conventional...
In this paper, we show several connections between special functions arising from generalized Conway-Maxwell-Poisson (COM-Poisson) type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type ope...
As a follow-up to the inherent nature of Hadamard-Type Fractional Integro-differential problem, little is known about some asymptotic behaviors of solutions. In this paper, an integro-differential problem involving Hadamard fractional derivatives is...
This work explores the existence and uniqueness criteria for the solution of hybrid Caputo–Hadamard fractional sequential differential equations (HCHFSDEs) by employing Darbo’s fixed-point theorem. Fractional differential equations play a...
This paper focuses on studying the uniqueness of the mild solution for an abstract fractional differential equation. We use Banach’s fixed point theorem to prove this uniqueness. Additionally, we examine the stability properties of the equation...
General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and di...
A nonlocal analogue of the biharmonic operator with involution-type transformations was considered. For the corresponding biharmonic equation with involution, we investigated the solvability of boundary value problems with a fractional-order boundary...
In this paper, we studied the existence results for solutions of a new class of the fractional boundary value problem in the Caputo–Hadamard settings. Moreover, boundary conditions of this fractional problem were formulated as the mixed multi-order H...
In this paper, we provide a collocation spectral scheme for systems of nonlinear Caputo–Hadamard differential equations. Since the Caputo–Hadamard operators contain logarithmic kernels, their solutions can not be well approximated using t...
In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary con...
In this paper, we present the preliminaries of ( p , q ) -calculus for functions of two variables. Furthermore, we prove some new Hermite-Hadamard integral-type inequalities for convex functions on coordinates over [ a , b ] × [ c ,...
This paper is concerned with the existence and uniqueness of solutions for a Hilfer–Hadamard fractional differential equation, supplemented with mixed nonlocal (multi-point, fractional integral multi-order and fractional derivative multi-order) bound...
In this work, we introduce new definitions of left and right-sides generalized conformable K-fractional derivatives and integrals. We also prove new identities associated with the left and right-sides of the Hermite-Hadamard-Fejér type inequal...
This paper studies the existence and uniqueness of solutions for a new coupled system of nonlinear sequential Caputo and Hadamard fractional differential equations with coupled separated boundary conditions, which include as special cases the well-kn...
This paper contains a variety of new integral inequalities for (s,m)-convex functions using Caputo fractional derivatives and Caputo–Fabrizio integral operators. Various generalizations of Hermite–Hadamard-type inequalities containing Cap...
We consider the predictor-corrector numerical methods for solving Caputo–Hadamard fractional differential equations with the graded meshes logtj=loga+logtNajNr,j=0,1,2,…,N with a≥1 and r≥1, where loga=logt0<logt1<⋯<logtN=logT is a partition...
For fractional-order systems, observer design is remarkable for the estimation of unavailable states from measurable outputs. In addition, the nonlinear dynamics and the presence of parameters that can vary over different operating conditions or time...
The subject of this paper is the existence, uniqueness and stability of solutions for a new sequential Van der Pol–Duffing (VdPD) jerk fractional differential oscillator with Caputo–Hadamard derivatives. The arguments are based upon the B...
In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions...
The aim of this article is to introduce analytical and approximate techniques to obtain the solution of time-fractional Navier–Stokes equations. This proposed technique consists is coupling the homotopy perturbation method (HPM) and Laplace tra...
In the present research, we initiate the study of boundary value problems for sequential Riemann–Liouville and Hadamard–Caputo fractional derivatives, supplemented with iterated fractional integral boundary conditions. Firstly, we convert the given n...
In this article, a new linear extended multiplier operator is defined utilizing the q-Choi–Saigo–Srivastava operator and the q-derivative. Two generalized subclasses of q—uniformly convex and starlike functions of order δ&mdas...
This paper investigates the problem of observer-based control for a class of nonlinear systems described by the Caputo–Hadamard fractional-order derivative. Given the growing interest in fractional-order systems for their ability to capture com...
We investigate a class of boundary value problems (BVPs) involving an impulsive fractional integro-differential equation (IF-IDE) with the Caputo–Hadamard fractional derivative (C-HFD). We employ some fixed-point theorems (FPTs) to study the ex...
This study aims to prove the existence and uniqueness of the (ω,c)-periodic solution as a specific solution to Hadamard impulsive boundary value integro-differential equations with fixed lower limits. The results are proven using the Banach con...
This study investigates fuzzy fixed points and fuzzy best proximity points for fuzzy mappings within the newly introduced framework θ-fuzzy metric spaces that extends various existing fuzzy metric spaces. We establish novel fixed-point and best...
This paper investigates the analytical properties of multiplicative generalized proportional σ-Riemann–Liouville fractional integrals and the corresponding Hermite–Hadamard-type inequalities. Central to our study are two key notions...
In this paper, we investigate an initial value problem for a nonlinear fractional differential equation on an infinite interval. The differential operator is taken in the Hadamard sense and the nonlinear term involves two lower-order fractional deriv...
In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for n-times differentiable functions whose absolute values of n-th derivatives are (α,m)-convex function. The results obtained in this paper are extensio...
We investigate the existence criteria for solutions of a nonlinear coupled system of Hilfer–Hadamard fractional differential equations of different orders complemented with nonlocal coupled Hadamard fractional integral boundary conditions. The...
This article deals with some existence and uniqueness result of random solutions for some coupled systems of Hilfer and Hilfer–Hadamard fractional differential equations with random effects. Some applications are made of generalizations of clas...
In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and...
This paper aims to find Hermite–Hadamard-type inequalities for a generalized notion of integrals called q−h-integrals. Inequalities for q-integrals can be deduced by taking h=0 and are connected with several known results of q-Hermite&nda...
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