In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate generalized Caputo fractional derivative (GCFD). Convergence order for (4−α), where α(0<α<1) of GCFD. The local truncation error also provided. Then, we adopt developed establish difference solution advection–diffusion equation with Dirichlet boundary conditions. Furthe...

Abstract In this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using concept of weak minima. Multiobjective find their applications in economic planning, flight control design, industrial process control, space structures, production inventory, advertising investment, impu...

*Correspondence: [email protected] 1Department of Mathematical Sciences, UAE University, P.O. Box 15551, Al Ain, UAE Full list of author information is available at the end of the article Abstract In this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog....

Abstract In this research, we first investigate the existence of solutions for a new fractional boundary value problem in Liouville–Caputo setting with mixed integro-derivative conditions. To do this, Kuratowski’s measure noncompactness and Sadovskii’s fixed point theorem are our tools to reach aim. sequel, discuss continuous dependence on parameters by means generalized Gronwall inequality. Mo...

this work is devoted to the study of global solution for initialvalue problem of interval fractional integrodifferential equationsinvolving caputo-fabrizio fractional derivative without singularkernel admitting only the existence of a lower solution or an uppersolution. our method is based on fixed point in partially orderedsets. in this study, we guaranty the existence of special kind ofinterv...

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...

In the presented research, uniqueness and existence of a mild solution for fractional system semilinear evolution equations with infinite delay an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative non-integer-order 1<??2 parameter 0<?<1 used to establish our model. ?-Laplace transform strongly continuous cosine sine families uniformly bounde...

This paper deals with the study of linear systems of fractional differential equations such as the following system: 0096-3 doi:10 * Co E-m Y ða 1⁄4 AðxÞY þ BðxÞ; ð1Þ where Y ða is the Riemann–Liouville or the Caputo fractional derivative of order a (0 < a 5 1), and AðxÞ 1⁄4 a11ðxÞ a1nðxÞ . . . . . . . . . an1ðxÞ annðxÞ 0BBBBBB@ 1CCCCCCA; BðxÞ 1⁄4 b1ðxÞ . . . . . . . . . bnðxÞ 0BBBBBB@ 1CCCCCCA...

He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...