This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized integro-differential boundary conditions by utilizing contraction principle Banach Leray–Schauder fixed point theorems. Moreover, two different approaches, Hyers–Ulam stabilities are also discussed. Different ordinary third order (e.g., initial, an...

In this article, we study a class of Hadamard fractional differential equations and give sufficient conditions on the existence of local and global of solutions.

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

This paper presents a novel approach by introducing set of operators known as the left and right generalized tempered fractional integral operators. These are utilized to establish new Hermite–Hadamard inequalities for convex functions well multiplication two functions. Additionally, this gives useful identities involving operator differentiable By leveraging these identities, our results consi...

The principal motivation of this paper is to establish a new integral equality related k-Riemann Liouville fractional operator. Employing equality, we present several inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard inequality. Additionally, some novel cases the established results different kinds derived. This sums up Riemann–Liouville and Hermit...

This study deals with a novel class of mean-type inequalities by employing fractional calculus and convexity theory. The high correlation between symmetry increases its significance. In this paper, we first establish an identity that is crucial in investigating mean inequalities. Then, the main results involving error estimation Hermite–Hadamard inequality for composite convex functions via gen...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....

Banach algebras defined by fractional Mikhlin-type conditions are continuously contained in Besov spaces, in such a way that the difference between the corresponding degrees of derivation can be made arbitrarily small. In this note a proof of this inclusion is given which is based on the Hadamard fractional operator and its adjoint integration operator on the positive half-line. §