A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered a...

Abstract We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial of Sturm-Liouville type. first prove existence uniqueness solutions STFPEs on an open bounded interval their regularity. Then we show to a quadratic problem. derive adjoint problem using the right-Caputo derivative in tim...

In this paper, we propose a mathematical study to simulate the dynamics of alkali–silica reaction (ASR) by using Caputo fractional derivative. We solve non-linear fractional-order system containing six differential equations understand ASR. For proving existence unique solution, use some recent novel properties Mittag–Leffler function along with fixed point theory. The stability proposed is als...

Sufficient conditions for extremum of fractional variational problems are formulated with the help Caputo derivatives. The Euler–Lagrange equation is defined in sense and Jacobi derived using this. Again, Wierstrass integral considered functional obtained from transversality conditions. Further, Taylor’s series expansion derivatives integral, Legendre’s sufficient condition problem established....

In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, apply Schaefer’s fixed point theorem. Furthermore, present Lyapunov inequality for corresponding problem.

The prime aim of the present paper is to continue developing theory tempered fractional integrals and derivatives a function with respect another function. This combines calculus $\Psi$-fractional calculus, both which have found applications in topics including continuous time random walks. After studying basic $\Psi$-tempered operators, we prove mean value theorems Taylor's for Riemann--Liouvi...