Since Al-Salam [1] and Agarwal [2] introduced the fractional q-difference calculus, the theory of fractional q-difference calculus itself and nonlinear fractional q-difference equation boundary value problems have been extensively investigated by many researchers. For some recent developments on fractional q-difference calculus and boundary value problems of fractional q-difference equations, s...

Differential equations with fractional derivative are being extensively used in the modelling of transmission many infective diseases like HIV, Ebola, and COVID-19. Analytical solutions unreachable for a wide range such kind equations. Stability theory sense Ulam is essential as it provides approximate analytical solutions. In this article, we utilize some fixed point theorem (FPT) to investiga...

The purpose of this paper is to give and prove the fundamental theorem conformable fractional calculus which given only in previous associated papers for differentiable functions, then we scrutinize existence uniqueness solutions some semilinear Cauchy problems nonlocal integrodifferential or differential equations their nonlinear terms include derivative integral. Two examples are investigated...

In this article we investigate the existence of extremal(maximal and minimal) solutions for the following coupled system of integrodifferential equations of fractional order with the given boundary conditions of the form  Du(t) + f1(t, v(t), I v(t)) = 0, 0 < t < 1, Dv(t) + f2(t, u(t), I u(t)) = 0, 0 < t < 1, u(0) = 0, u′(1) = 0, v(0) = 0, v′(1) = 0. where 1 < α, β ≤ 2 and f1, f2 : [0, 1] × ...

In this paper, the successive overrelaxation iteration and the variation of parameters formula are used to discuss the stability of linear and nonlinear Volterra integrodifferential equations. Some sufficient conditions are obtained, such that the trivial solution of the Volterra integrodifferential equations is asymptotically stable; these stability conditions are given directly from the coeff...