In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

We study weak-type (1, 1) weighted inequalities for the fractional integral operator Iα. We show that the fractional maximal operatorMα controls these inequalities when the weight is radially decreasing. However, we exhibit some counterexamples which show that Mα is not appropriate for this control on general weights. We do provide, nevertheless, some positive results related to this problem by...

Convexity assumptions for fractional programming of variational type are relaxed to generalized invexity. The sufficient optimality conditions are employed to construct a mixed dual programming problem. It will involve the Wolfe type dual and Mond-Weir type dual as its special situations. Several duality theorems concerning weak, strong, and strict converse duality under the framework in mixed ...

In this study, we focus on the newly introduced concept of LR-convex interval-valued functions to establish new variants Hermite–Hadamard (H-H) type and Pachpatte inequalities for Riemann–Liouville fractional integrals. By presenting some numerical examples, also verify correctness results that have derived in paper. Because results, which are related differintegral ϱ1+ϱ22 type, novel context f...

The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It shown that the derivative integral operators are bounded. Some fundamental characteristics of new operators, such as semi-group inverse characteristics, studied. As special cases these novel several already well known in literature acquired. generalized Laplace transform evaluated. By ...

By means of a certain extended fractional differintegral operator Ω (λ,p) z (−∞ < λ < p + 1; p ∈ N), the authors introduce and investigate two new subclasses of p-valently analytic functions of complex order. The various results obtained here for each of these function classes include coefficient inequalities and the consequent inclusion relationships involving the neighborhoods of the p-valent...