In this article, we employed Mönch’s fixed point theorem to investigate the existence of solutions for a system nonlinear Hadamard fractional differential equations and nonlocal non-conserved boundary conditions in terms integral. Followed by study stability solution using Ulam-Hyres technique. This concludes with an applied numerical example that helps understanding theoretical results obtained.

In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicativelys-preinvex functions. We also obtain some new inequalities involving multiplicative integralsby using some properties of multiplicatively s-preinvex and preinvex functions.

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

The main objective of this paper is to establish some new variants the Jensen–Mercer inequality via harmonically strongly convex function. We also propose fractional analogues Hermite–Hadamard–Jensen–Mercer-like inequalities using AB integrals. In order obtain our results, we derive integral identities. To demonstrate significance present interesting applications special means and error bounds ...

Singular integral equation method is one of the most effective numerical methods solving a plane crack problem in fracture mechanics. Depending on the choice of the density function, very often a higher order of sigularity appears in the equation, and we need to give a proper meaning of the integration. In this article we address the Hadamard finite part integral and how it is used to solve the...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...