This paper presents new bounds for the left and right Fractional mean-square stochastic integrals based on convex stochastic processes. Then a range is proposed that includes a linear combination of the left and right Fractional mean-square stochastic integrals. Finally, the previous results presented in this subject are improved.

Fejer Hadamard inequality is generalization of Hadamard inequality. In this paper we prove certain Fejer Hadamard inequalities for k-Fractional integrals. We deduce Fejer Hadamard-type inequalities for Riemann-Liouville Fractional integrals. Also as special case Hadamard inequalities fork-Fractional as well as Fractional integrals are given.

In this paper, we investigate the solutions of a class of-Hilfer Fractional differential equations with the initial values in the sense of-Fractional integral by using the successive approximation techniques. Next, the continuous dependence of a solution for the given Cauchy-type problem is presented.

In this paper, we investigate the Bullen inequality in the context of Fractional integrals with exponential kernels. Building upon the foundational works in the field, we first introduce a new integral identity. From this identity, we derive several novel Bullen-type inequalities for differentiable convex functions. To validate our theoretical findings, we provide a numerical example along with graphical representations, demonstrating the accuracy and applicability of our results. The results obtained are not only new for the Fractional integrals considered in our study, but as \(\alpha\) approaches 1, we also derive additional novel results for the classical integral.

In this study, beta-derived Sturm–Liouville problems are discussed. First, the existence and uniqueness problem for such equations is discussed. Then, self-adjointness is obtained with the help of boundary conditions. Eigenfunction expansion was obtained with the help of characteristic determinants and Green’s function. Finally, an example is given showing the theoretical results obtained.

This article is devoted to investigate the anlysis for the solution for a class of linear and nonlinear Caputo Fractional FredholmVolterra integro-differential equations with multiple delays. The convergence and stability analysis for these equations are investigated.

In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized Fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for $k$-Riemann-Liouville Fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition $f^{\prime }(a+b-x)\geq f^{\prime }(x)$ for all $x\in \left[ a,\frac{a+b}{2}\right] $ instead of convexity.