*Correspondence: [email protected]; [email protected] 1School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou 550018, P.R. China 2Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P.R. China Full list of author information is available at the end of the article Abstract Motivated by the definition of geometric-arithmetically s-convex...

The current paper intends to report the existence and uniqueness of positive solutions for nonlinear pantograph Caputo–Hadamard fractional differential equations. As part a procedure, we transform specified equation into an equivalent integral equation. We show that this has solution by utilising Schauder fixed point theorem (SFPT) upper lower method. Another method proving singular is Banach (...

In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo operators, nonperiodic nonlocal integral boundary conditions. The results presented in study establish existence, uniqueness, Hyers–Ulam (HU) stability of solution to proposed equation. We achieved our main result by using Banach contraction mapping principle Kraso...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

In this paper, we present weighted integral inequalities of Hermite-Hadamard type for differentiable preinvex and prequasiinvex functions. Our results, on the one hand, give a weighted generalization of recent results for preinvex functions and, on the other hand, extend several results connected with the Hermite-Hadamard type integral inequalities. Applications of the obtained results are prov...

In this paper, the authors define a new generic class of functions involving certain modified Fox–Wright function. A useful identity using fractional integrals and function with two parameters is also found. Applying as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by above-mentioned functions. Some special cases are derived relevant details. Moreover, in or...

In this study, a new identity involving conformable fractional integrals is given. Then, by using this identity, some new Hermite-Hadamard type inequalities for conformable fractional integrals have been developed.

We propose the concept of up and down harmonically convex mapping for fuzzy-number-valued as our main goal in this work. With help fuzzy-number convexity fuzzy fractional integral operator, we also show results Hermite–Hadamard (H–H) inequality, Fejér type some other related versions inequalities. Moreover, examples are presented to discuss validity results. The from new technique how suggested...

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 the present work, we introduce two new local fractional integral operators involving Mittag–Leffler kernel on Yang’s fractal sets. Then, study related generalized Hermite–Hadamard-type inequality using (E,h)-convexity and obtain identities pertaining to these operators, respective first- second-order derivatives are given. terms of applications, provide some trapezoid-type inequalities for (...