On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example

P A POSITIVE SOLUTIONS OF SUMMATION BOUNDARY VALUE PROBLEM FOR A GENERALIZED SECOND-ORDER DIFFERENCE EQUATION

Abstract: In this paper, by using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problem ∆ 2 y(t − 1) + a(t)f (y(t)) = 0, t ∈ {1, 2, ..., T }, where f is continuous, T ≥ 3 is a fixed positive integer, η ∈ {1, 2, ..., T − 1}, and ∆y(t − 1) = y(t) − y(t − 1) is the forward difference operator. We show the existence of at least one positive solution if f is neither superlinear and sublinear by applying the fixed point theorem in cones

On Generalization of Different Integral Inequalities for Harmonically Convex Functions

In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers

On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables

In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann-Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.King Mongkut's University of Technology North Bangkok [KMUTNB-62-KNOW-26]This research was funded by King Mongkut's University of Technology North Bangkok. Contract no. KMUTNB-62-KNOW-26.WOS:0007017717000012-s2.0-8511580040

Analysis of Existence and Stability Results for Impulsive Fractional Integro-Differential Equations Involving the Atangana–Baleanu–Caputo Derivative under Integral Boundary Conditions

In this study, we consider the existence results of solutions of impulsive Atangana–Baleanu–Caputo ABC fractional integro-differential equations with integral boundary conditions. Krasnoselskii’s fixed-point theorem and the Banach contraction principle are used to prove the existence and uniqueness of results. Moreover, we also establish Hyers–Ulam stability for this problem. An example is also presented at the end

A Comprehensive Analysis of Hermite–Hadamard Type Inequalities via Generalized Preinvex Functions

The principal objective of this article is to introduce the idea of a new class of n-polynomial convex functions which we call n-polynomial s-type m-preinvex function. We establish a new variant of the well-known Hermite–Hadamard inequality in the mode of the newly introduced concept. To add more insight into the newly introduced concept, we have discussed some algebraic properties and examples as well. Besides, we discuss a few new exceptional cases for the derived results, which make us realize that the results of this paper are the speculations and expansions of some recently known outcomes. The immeasurable concepts and chasmic tools of this paper may invigorate and revitalize additional research in this mesmerizing and absorbing field

Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings

In this paper, we prove Hermite–Hadamard–Mercer inequalities, which is a new version of the Hermite–Hadamard inequalities for harmonically convex functions. We also prove Hermite–Hadamard–Mercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities

On Generalization of Different Integral Inequalities for Harmonically Convex Functions

In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers

A Comprehensive Analysis of Hermite–Hadamard Type Inequalities via Generalized Preinvex Functions

The principal objective of this article is to introduce the idea of a new class of n-polynomial convex functions which we call n-polynomial s-type m-preinvex function. We establish a new variant of the well-known Hermite–Hadamard inequality in the mode of the newly introduced concept. To add more insight into the newly introduced concept, we have discussed some algebraic properties and examples as well. Besides, we discuss a few new exceptional cases for the derived results, which make us realize that the results of this paper are the speculations and expansions of some recently known outcomes. The immeasurable concepts and chasmic tools of this paper may invigorate and revitalize additional research in this mesmerizing and absorbing field

Impact of bioconvection and chemical reaction on MHD nanofluid flow due to exponential stretching sheet

Thermal management is a crucial task in the present era of miniatures and other gadgets of compact heat density. This communication presents the momentum and thermal transportation of nanofluid flow over a sheet that stretches exponentially. The fluid moves through a porous matrix in the presence of a magnetic field that is perpendicular to the flow direction. To achieve the main objective of efficient thermal transportation with increased thermal conductivity, the possible settling of nano entities is avoided with the bioconvection of microorganisms. Furthermore, thermal radiation, heat source dissipation, and activation energy are also considered. The formulation in the form of a partial differential equation is transmuted into an ordinary differential form with the implementation of appropriate similarity variables. Numerical treatment involving Runge–Kutta along with the shooting technique method was chosen to resolve the boundary values problem. To elucidate the physical insights of the problem, computational code was run for suitable ranges of the involved parameters. The fluid temperature directly rose with the buoyancy ratio parameter, Rayleigh number, Brownian motion parameter, and thermophoresis parameter. Thus, thermal transportation enhances with the inclusion of nano entities and the bioconvection of microorganisms. The findings are useful for heat exchangers working in various technological processors. The validation of the obtained results is also assured through comparison with the existing result. The satisfactory concurrence was also observed while comparing the present symmetrical results with the existing literature.Published versionThis research was funded by King Mongkut’s University of Technology North Bangkok. Contract no. KMUTNB-63-KNOW-19