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 this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...

In this article, we introduce the fractional differential systems in the sense of the Weber fractional derivatives and study the asymptotic stability of these systems. We present the stability regions and then compare the stability regions of fractional differential systems with the Riemann-Liouville and Weber fractional derivatives.

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...

Abstract In this paper, we study a nonlinear fractional p-Laplacian boundary value problem containing both left Riemann–Liouville and right Caputo derivatives with initial integral conditions. Some new results on the existence uniqueness of solution for model are obtained as well Ulam stability solutions. Two examples provided to show applicability our results.

In this paper, we present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella functions, by using the extended Bessel due to Boudjelkha [?]. Some recurrence relations, transformation formulas, Mellin transform integral representations are obtained for these generalizations. Further, an extension Riemann-Liouville fractional deri...

In this paper, under some super- and sub-linear growth conditions, we study the existence of positive solutions for a high-order Riemann–Liouville type fractional integral boundary value problem involving derivatives. Our analysis methods are based on fixed point index nonsymmetric property Green function. Additionally, provide valid examples to illustrate our main results.

In this paper, we study a new nonlinear sequential differential prob-
 lem with nonlocal integral conditions that involve convergent series. The
 problem involves two fractional order operators: Riemann-Liouville inte-
 gral, Caputo and derivatives. We prove an existence
 uniqueness result. Also, existence end our
 paper by presenting some illustrative examples.