Integral inequalities have accumulated a comprehensive and prolific field of research within mathematical interpretations. In recent times, strategies fractional calculus become the subject intensive in historical contemporary generations because their applications various branches science. this paper, we concentrate on establishing Hermite–Hadamard Pachpatte-type integral with aid two differen...

In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results  how that the simplicity and efficiency of this method.

In this paper, we derive a new extension of Hermite-Hadamard's inequality via k-Riemann-Liouville fractional integrals. Two new k-fractional integral identities are also derived. Then, using these identities as an auxiliary result, we obtain some new k-fractional bounds which involve k-Appell's hypergeometric functions. These bounds can be viewed as new k-fractional estimations of trapezoidal a...

In this paper, we consider two new uniqueness results for fuzzy fractional differential equations (FFDEs) involving Riemann-Liouville generalized H-differentiability with the Nagumo-type condition and the Krasnoselskii-Krein-type condition. To this purpose, the equivalent integral forms of FFDEs are determined and then these are used to study the convergence of the Picard successive approximati...

In this paper, we study the existence of positive solutions for a system fractional differential equations with ?-Laplacian operators, Riemann–Liouville derivatives diverse orders and general nonlinearities which depend on several integrals differing orders, supplemented nonlocal coupled boundary conditions containing Riemann–Stieltjes varied derivatives. The from are continuous nonnegative fun...

Applying Baxter’s method of the Q-operator to the set of Sekiguchi’s commuting partial differential operators we show that Jack polynomials P (1/g) λ (x1, . . . , xn) are eigenfunctions of a one-parameter family of integral operators Qz. The operators Qz are expressed in terms of the Dirichlet-Liouville n-dimensional beta integral. From a composition of n operators Qzk we construct an integral ...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

In this paper, some new estimates on Fej?r sort inequalities via Riemann Liouville fractional integral for the products of two harmonically-convex functions are obtained.

Applying Baxter’s method of the Q-operator to the set of Sekiguchi’s commuting partial differential operators we show that Jack’s symmetric polynomials P (1/g) λ (x1, . . . , xn) are eigenfunctions of a one-parameter family of integral operators Qz . The operators Qz are expressed in terms of the Dirichlet-Liouville n-dimensional beta integral. From a composition of n operators Qzk we construct...

Abstract In this paper, the numerical method for solving Abel’s integral equations is presented. This method is based on fractional calculus. Also, Chebyshev polynomials are utilized to apply fractional properties for solving Abel’s integral equations of the first and second kind. The fractional operator is considered in the sense of RiemannLiouville. Although Abel’s integral equations as singu...