Models of bio-mathematics are experimental systems that recreate aspects human tissue function, diseases or virus. In this research, a new operational matrix based on the Laguerre wavelets is introduced for arbitrary-order susceptible-infected-recovered (SIR) epidemic dynamical system childhood diseases. An exact mechanism Riemann–Liouville arbitrary integral operator explained where derivative...

The paper is concerned with existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann–Liouville fractional derivative. By noncompact measure method, we obtain some sufficient conditions to ensure the existence of mild solution. Our results are new and more general to known results. Nowadays, fractional calculus receives increasing at...

In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applica...

In this work, the fractional Lie symmetry method is used to find exact solutions of time-fractional coupled Drinfeld-Sokolov-Wilson equations with Riemann-Liouville derivative. Time-fractional are obtained by replacing first-order time derivative derivatives (FD) order $\alpha$ in classical (DSW) model. Using method, generators obtained. With help generators, FCDSW reduced into ordinary differe...

In this paper, we study the existence of a solution for nonlinear implicit fractional differential equation type D?u(t) = f (t, u(t),D?u(t)), with Riemann-Liouville derivative via different boundary conditions u(0) u(T), and three point ?1u(?) u(T) ?2u(?), where T > 0, t ? I [0,T], 0 < 1, T, ?1 ?2 1.

In this paper, we present a qualitative study of an implicit fractional differential equation involving Riemann–Liouville derivative with delay and its corresponding integral equation. Under some sufficient conditions, establish the global local existence results for that problem by applying fixed point theorems. addition, have investigated continuous integrable solutions problem. Moreover, dis...

Abstract In this paper, we study a system of nonlinear Riemann–Liouville fractional differential equations with delays. First, define in an appropriate way initial conditions which are deeply connected the derivative used. We introduce generalization practical stability call time. Several sufficient for time obtained using Lyapunov functions and modified Razumikhin technique. Two types derivati...

In this paper, a hybrid variable-order mathematical model for multi-vaccination COVID-19 is analyzed. The derivative defined as linear combination of the integral Riemann–Liouville and Caputo derivative. A symmetry parameter ? presented in order to be consistent with physical problem. existence, uniqueness, boundedness positivity proposed are given. Moreover, stability discussed. theta finite d...

The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of time orders we provide the fundamental solution, that is still a probability density, in terms of an integral of Laplace type. The kernel depends on the typ...

There are many functions which are continuous everywhere but non-differentiable at someor all points such functions are termed as unreachable functions. Graphs representing suchunreachable functions are called unreachable graphs. For example ECG is such an unreachable graph. Classical calculus fails in their characterization as derivatives do not exist at the unreachable points. Such unreachabl...