Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...

‎in this paper‎, ‎a spectral tau method for solving fractional riccati‎ ‎differential equations is considered‎. ‎this technique describes‎ ‎converting of a given fractional riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎we use fractional derivatives in the caputo form‎. ‎convergence analysis of the proposed method is given an...

<abstract><p>In this paper, we consider the time-fractional telegraph equation of distributed order in higher spatial dimensions, where time derivative is sense Hilfer, thus interpolating between Riemann-Liouville and Caputo fractional derivatives. By employing techniques Fourier, Laplace, Mellin transforms, obtain a representation solution Cauchy problem associated with terms convo...

Abstract In this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed differential equation that involves Riemann–Liouville derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with composition three operators. After that, its stability analysis Ulam–Hyers rele...

New properties of the first‐order Riemann–Liouville fractional integrals are proved and derivatives for equivalence class functions in analyzed. Solutions, normal solutions, generalized solutions initial value problems (IVPs) nonlinear differential equations (FDEs) with fraction introduced. The equivalences between FDEs corresponding (Volterra) integral established based on solutions. results e...

In recent decades, various types of control techniques have been proposed for use in power systems. Among them, the a proportional–integral–derivative (PID) controller is widely recognized as an effective technique. The generalized type this fractional-order PID (FOPID) controller. This provides wider range stability area due to fractional orders integrals and derivatives. These controllers sig...

Exploring the possible links between the mathematical field of fractional calculus and the electromagnetic theory has been one of the topics of our research interests in recent years. We have studied the possibility of bringing the tools of fractional calculus and electromagnetic theory together, and have explored and developed the topic of fractional paradigm in electromagnetic theory (see e.g...