This paper focuses on studying the uniqueness of mild solution for an abstract fractional differential equation. We use Banach’s fixed point theorem to prove this uniqueness. Additionally, we examine stability properties equation using Ulam’s stability. To analyze these properties, consider involvement Hadamard derivatives. Throughout study, put significant emphasis role and resolvent operators. Furthermore, investigate Ulam-type by providing examples partial equations that incorporate

The significant motivation behind this research article is to utilize a technique depending upon acertain variant of the integral transform (Fourier and Laplace) investigate basic solution for theDirichlet problem with constant boundary conditions. time-fractional derivative one-dimensional,the equation advection-diffusion Liouville-Caputo fractional in line fragment areintroduced. We also illustrate results using graphical representations

The aim of this paper is to obtain some new results related Minkowski fractional integral inequality and other integra l inequalities using Saigo .

In this paper, using Hadamard fractional integral, we establish two main new result on integral inequalities by considering the extended Chebyshev functional in case of synchronous function. The first concerns with some one parameter and other parameter.

The main aim of this paper is to establish some new fractional integral inequalities Grüss-type via the Saigo operator.

In this paper, we obtain results related to Minkowski fractional integral inequality using generalized k-fractional operator is in terms of the Gauss hypergeometric function.

The main objective of the paper is to solve ordinary fractional differential equations using Elzaki and Sumudu transform. Moreover some are solved by presented method. Using different types operators existing methods have been extended applied for equations.

The main objective of this paper is to prove the existence and uniqueness mild solution for abstract differential equations by using resolvent operators fixed point theorem.Moreover, we studied some examples on partial equation with Caputo-Fabrizio derivative.

The Caputo–Fabrizio fractional integral operator is one of the important notions calculus. It involved in numerous illustrative and practical issues. main goal this paper to investigate weighted inequalities using with non-singular e−1−δδ(ϰ−s), 0<δ<1. Furthermore, based on a family n positive functions defined [0,∞), we some new extensions inequalities.

In this paper, using generalized k-fractional integral operator (in terms of the Gauss hypergeometric function), we establish new results on inequalities by considering extended Chebyshev functional in case synchronous function and some other inequalities.

using generalized Katugampola fractional integral operator.

In this paper, we deal with the Caputo–Fabrizio fractional integral operator a nonsingular kernel and establish some new inequalities for Chebyshev functional in case of synchronous function by employing integral. Moreover, several extended considering are discussed. addition, obtain three positive functions involving same operator.

The main objective of present investigation is to obtain some Minkowski-type fractional integral inequalities using generalised proportional Hadamard operators which introduced by Rahman et al. in the paper (Certain via generalized operators), Advances Differential Equations, 2019, 454(2019). In addition, we establish other for positive and continuous functions.

In the present paper, we study uniqueness theorem of solution fractional differential equation with initial condition by using Bihari's and Medved inequality.

In this article, we establish some of the Pólya–Szegö and Minkowsky-type fractional integral inequalities by considering Caputo–Fabrizio integral. Moreover, give special cases inequalities.

The main objective of this paper is to use the generalized proportional Hadamard fractional integral operator establish some new inequalities for extended Chebyshev functionals. In addition, we investigate positive continuous functions by employing a operator. findings study are theoretical but have potential help solve additional practical problems in mathematical physics, statistics, and approximation theory.

In this paper, we establish some new inequalities of expectation and variance continuous random variables by using the Hadamard fractional integral operator.

<p>In this article, we employ the Laplace transform (LT) method to study fractional differential equations with problem of displacement motion mass for free oscillations, damped forced and oscillations (without damping). These problems are solved by using Caputo Atangana-Baleanu (AB) derivatives, which useful derivative operators consist a non-singular kernel efficient in solving non-local problems. The mathematical modelling is presented form. Moreover, some examples solved.</p>

Abstract In this article, the main objective is to establish Grüss-type fractional integral inequalities by employing Caputo-Fabrizio integral.

In the present paper, we establish some new fractional integral inequalities similar to P$\acute{o}$lya-Szeg$\ddot{o}$ inequality and related Minkowsky by using Hadamard operator. Also, discuss few spacial cases of these inequalities.

The aim of the present paper is to obtain some new fractional integral inequalities for convex functions. Saigo operator used establish results.