Abstract We examine a class of nonlinear fractional Mathieu equations with damping term. The equation is an important mathematical physics as it has many applications in various fields the physical sciences. By utilizing Schauder’s fixed-point theorem, existence arises solutions for proposed Hilfer–Katugampola derivative, and application additionally examined. Two examples guarantee obtained re...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

Abstract In this article, we debate the existence of solutions for a nonlinear Hilfer fractional differential inclusion with nonlocal Erdélyi–Kober integral boundary conditions (FIBC). Both cases convex- and nonconvex-valued right-hand side are considered. Our obtained results new in framework derivative FIBC via fixed point theorems (FPTs) set-valued analysis. Some pertinent examples demonstra...

In this paper, images of the tempered Ψ-Hilfer fractional integral and Ψ-Caputo derivative under generalized Laplace transform are derived. The results applied to find a solution an initial value problem for nonhomogeneous linear differential equation with order α n− 1 <α<n N. An illustrative example is given 0 <α<1 comparing solutions same but different tempering Ψ.

In this paper, we study the existence and uniqueness of mild solutions for nonlinear fractional integro-differential equations (FIDEs) subject to nonlocal integral boundary conditions (nonlocal IBC) in frame a ξ-Hilfer derivative (FDs). Further, discuss different kinds stability Ulam-Hyers (UH) given problem. Using fixed point theorems (FPT's) together with generalized Gronwall inequality desir...